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Prof .E.P.Lewis 













This course of four Lectures on the Electromagnet 
was delivered in February, 1890, before the Society of 
Arts, London, and constituted one of the sets of " Can- 
tor" Lectures of the Session 1889-90. This volume is 
reprinted with the direct sanction of the Author, who 
has revised the text for republication. It is the only 
authorized American edition. 



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Introductory ; Historical Sketch ; Generalities Concerning Electro- 
magnets ; Typical Forms ; Polarity ; Uses in General ; The Proper- 
ties of Iron; Methods of Measuring Permeability; Traction Methods; 
Curves of Magnetization and Permeability; The Law of the Electro- 
magnet; Hysteresis; Fallacies arid Facts about Electromagnets. 


General Principles of Design and Construction ; Principles of the 
Magnetic Circuit. 


Calculation of Excitation, Leakage, etc. ; Rules for Estimating Magnetic 


Special Designs; Winding of the Copper; Windings for Constant 
Pressure and for Constant Current ; Miscellaneous Rules about 
Winding; Specifications of Electromagnets; Amateur Rule about 
Resistance of Electromagnet and Battery; Forms of Electromagnets; 
Effect of Size of Coils ; Effect of Position of Coils ; Effect of Shape 
of Section; Effect of Distance between Poles ; Researches of Prof . 
Hughes; Position and Form of Armature; Pole-Pieces on -Horse- 
shoe Magnets ; Contrasts between Electromagnets and Permanent 
Magnets; Electromagnets for Maximum Traction; Electromagnets 
for Maximum Range of Attraction ; Electromagnets of Minimum 
Weight ; A Useful Guiding Principle ; Electromagnets for Use with 
Alternating Currents ; Electromagnets for Quickest Action ; Con- 
necting Coils for Quickest Action ; Battery Grouping for Quickest 
Action ; Time-Constant of Electromagnets ; Short Cores vs. Long 


Electromagnetic Mechanism ; The Coil-and-Plunger; Effect of Using 
Coned Plunger ; Other Modes of Extending Range of Action; Modi- 
fications of the Coil-and-Plunger ; Differential Coil-and-Plunger ; 
Coil-and-Plunger Coil ; Intermediate Forms ; Action of Magnetic 
Field on Small Iron Sphere; Sectioned Coils with Plunger; Winding 
of Tubular Coils and Electromagnets ; Extension of Range by Oblique 
Approach ; Polarized Mechanism ; Uses of Permanent Magnets ; 
Electromagnetic Mechanism; Moving Coil in Permanent Magnetic 
Field; Magnetic Adherence; Repulsion Mechanism; Electromag- 
netic Vibrators ; Indicator Movements ; The Study of Electromag- 
netic Mechanism; Suppression of Sparking; Conclusion, 

f, * m* t*V rv * 




Sturgeon's First Electromagnet, 18 

Sturgeon's Straight-Bar Electromagnet, 19 

Sturgeon's Lecture-Table Electromagnet, 25 

Henry's Electromagnet, . 35 

Henry's Experimental Electromagnet, 36 

Joule's Electromagnet, 41 

Joule's Cylindrical Electromagnet, 45 

Roberts' Electromagnet, 46 

Joule's Zigzag Electromagnet, *. 46 

Typical Two-Pole Electromagnet, 50 

Iron-Clad Electromagnet, 50 

Diagram Illustrating Relation of Magnetizing Circuit and Resulting 

Magnetic Force, 51 

Curves of Magnetization of Different Magnetic Materials, . . . .57 

Ring Method of Measuring Permeability (Rowland's Arrangement), . 60 

Bosanquet's Data of Magnetic Properties of Iron and Steel Rings, . . 62 

Hopkinson's Divided Bar Method of Measuring Magnetic Permeability, 64 

Curves of Magnetization of Iron, 66 

The Permeameter, 70 

Curves of Permeability, 73 

Curves of Hysteresis, 75 

Bosanquet's Verification of the Law of Traction, 90 

Stumpy Electromagnet, 97 

Experiment on Rounding Ends, 105 

Experiment of Detaching Armature, 105 

Lines of Force Running through Bar Magnet, 107 

Apparatus to Illustrate the Law of Inverse Squares, 113 

Deflection of Needle Caused by Bar Magnet Broadside on, . . .115 

Closed Magnetic Circuit, 116 

Divided Magnetic Circuit, 117 

Electromagnet with Armature in Contact, 119 

Electromagnet with Air-Gaps One Millimetre Wide, 119 

Electromagnet with Air-Gaps Several Millimetres Wide, . . . .121 

Electromagnet without Armature, .,,,,,, , , 131 



Contrasted Effect of Flat and Pointed Poles, 127 

Dub's Experiments with Pole- Pieces, 129 

Dub's Deflection Experiment, 130 

Deflecting a Steel Magnet Having Bifilar Suspension Pole-Piece on 

Near End 131 

Deflecting Steel Magnet Pole-Piece on Distant End, . . 131 

Experiment with Tubular Core and Iron Ring, . 

Exploring Polar Distribution with Small Iron Ball, . ... 137 

Iron Ball Attracted to Edge of Polar Face, 139 

Experiment on Leakage of Electromagnet, ... . 140 

Curves of Magnetization Plotted from Preceding, 143 

Curves of Flow of Magnetic Lines in Air from One Cylindrical Pole to 

Another, 146 

Diagram of Leakage Reluctances, 148 

Von Feilitzsch's Curves of Magnetization of Rods of Various Diameters, 152 

Ewing's Curves for Effect of Joints, 157 

Von Feilitzsch's Curves of Magnetization of Tubes, 159 

Club-Footed Electromagnet, 189 

Hughes' Electromagnet, . 195 

Experiment with Permanent Magnet, 200 

Electromagnetic Pop-Gun, 205 

Curves of Rise of Currents 211 

Curves of Rise of Current with Different Groupings of Battery, . .216 

Electromagnets of Relay and their Effects, 219 

Hjorth's Electromagnetic Mechanism, 224 

Action of Single Coil on Point Pole on Axis, 230 

Action along Axis of Single Coil, 230 

Action of Tubular Coil, 232 

Diagram of Force and Work of Coil-and-Plunger, 235 

Von Feilitzsch's Experiment on Plungers of Iron and Steel, . . .244 

Bruger's Experiments on Coils and Plungers, ...... 245 

Bruger's Experiments, Using Currents of Various Strengths, . . .245 

Plunger Electromagnet of Stevens and Hardy, 252 

Electromagnet of Brush Arc Lamp, 253 

Ayrton and Perry's Tubular Iron-Clad Electromagnet, . . . .254 

Froment's Equalizer with Stanhope Lever 261 

Davy's Mode of Controlling Armature by Spring 261 

Robert Houdin's Equalizer, 262 

Mechanism of Duboscq's Arc Lamp, 263 

Nickles' Magnetic Friction Gear, 271 

Forbes' Electromagnet, 272 

Electromagnetic Mechanism Working by Repulsion, 273 

Repulsion between Two Parallel Cores 273 





AMONG the great inventions which have originated in 
the lecture-room in which we are met are two of special 
interest to electricians the application of gutta-percha 
to the purpose of submarine telegraph cables, and the 
electromagnet. This latter invention was first publicly 
described, from the very platform on which I stand, on 
May 23, 1825, by William Sturgeon, whose paper is to 
be found in the forty-third volume of the Transactions 
of the Society of Arts. For this invention we may right- 
fully claim the very highest place. Electrical engineer- 
ing, the latest and most vigorous offshoot of applied 
science, embraces many branches. The dynamo for 
generating electric currents, the motor for transforming 
their energy back into work, the arc lamp, the electric 
bell, the telephone, the recent electromagnetic machin- 
ery for coal-mining, for the separation of ore, and many 


other electro-mechanical contrivances, come within the 
purview of the electrical engineer. In every one of 
these, and in many more of the useful applications of 
electricity, the central organ is an electromagnet. By 
means of this simple and familiar contrivance an iron 
core surrounded by a copper-wire coil mechanical ac- 
tions are produced at will, at a distance, under control, 
by the agency of electric currents. These mechanical 
actions are known to vary with the mass, form, and 
quality of the iron core, the quantity and disposition 
of the copper wire wound upon it, the quantity of 
electric current circulating around it, the form, quality, 
and distance of the iron armature upon which it aces. 
But the laws which govern the mechanical action in re- 
lation to these various matters are by no means well 
known, and, indeed, several of them have long been a 
matter of dispute. Gradually, however, that which has 
been vague and indeterminate becomes clear and pre- 
cise. The laws of the steady circulation of electric cur- 
rents, at one time altogether obscure, were cleared up 
by the discovery of the famous law of Ohm. Their ex- 
tension to the case of rapidly interrupted currents, such 
as are used in telegraphic working, was discovered by 
Helmholtz; while to Maxwell is due their future exten- 
sion to alternating, or, as they are sometimes called, 
undulatory currents. All this was purely electric work. 
But the law of the electromagnet was still undiscovered; 
the magnetic part of the problem was still buried in 
obscurity. The only exact reasoning about magnetism 
dealt with problems of another kind; it was couched in 
language of a misleading character; for the practical 


problems connected with the electromagnet it was worse 
than useless. The doctrine of two magnetic fluids dis- 
tributed over the end surfaces of magnets, under the 
sanction of the great names of Coulomb, of Poisson, 
and of Laplace, had unfortunately become recognized 
as an accepted part of science along with the law of in- 
verse squares. How greatly the progress of electromag- 
netic science has been impeded and retarded by the 
weight of these great names it is impossible now to 
gauge. We now know that for all purposes, save only 
those whose value lies in the domain of abstract mathe- 
matics, the doctrine of the two magnetic fluids is false 
and misleading. We know that magnetism, so far from 
residing on the end or surface of the magnet, is a prop- 
erty resident throughout the mass; that the internal, 
not the external, magnetization is the important fact to 
be considered; that the so-called free magnetism on the 
surface is, as it were, an accidental phenomenon; that 
the magnet is really most highly magnetized at those 
parts where there is least surface magnetization; finally, 
that the doctrine of surface distribution of fluids is ab- 
solutely incompetent to afford a basis of calculation such 
as is required by the electrical engineer. He requires 
rules to enable him not only to predict the lifting power 
of a given electromagnet, but also to guide him in de- 
signing and constructing electromagnets of special forms 
suitable for the various cases that arise in his practice. 
He wants in one place a strong electromagnet to hold 
on to its armature like a limpet to its native rock ; in 
another case he desires a magnet having a very long 
range of attraction, and wants a rule to guide him to 


the best design; in another he wants a special form 
having the most rapid action attainable; in yet another 
he must sacrifice everything else to attain maximum 
action with minimum weight. Toward the solution of 
such practical problems as these the old theory of mag- 
netism offered not the slightest aid. Its array of math- 
ematical symbols was a mockery. It was as though an 
engineer asking for rules to enable him to design the 
cylinder and piston of an engine were confronted with 
recipes how to estimate the cost of painting it. 

Gradually, however, new light dawned. It became 
customary, in spite of the mathematicians, to regard the 
magnetism of a magnet as something that traverses or 
circulates around a definite path, flowing more freely 
through such substances as iron than through other 
relatively non-magnetic materials. Analogies between 
the flow of electricity in an electrically conducting cir- 
cuit, and the passage of magnetic lines of force through 
circuits possessing magnetic conductivity, forced them- 
selves upon the minds of experimenters, and compelled 
a mode of thought quite other than that previously ac- 
cepted. So far back as 1821, Gumming 1 experimented 
on magnetic conductivity. The idea of a magnetic 
circuit was more or less familiar to Ritchie, 2 Sturgeon, 3 
Dove, 4 Dub, 5 and De La Rive, 6 the last-named of whom 

1 Camb. Phil. Trans., Apr. 2, 1821. 

2 Phil. Mag., series iii., vol. iii., p. 122. 
a Ann. ofElectr., xii., p. 217. 

* Pogg. Ann., xxix., p. 462, 1833. See aiso Pogg. Ann., xliii., p. 517, 1838. 

5 Dub, " Elektromagnetismus " (ed. 1861), p. 401 ; and Pogg. Ann., xc., p. 
440, 1853. 

8 De La Rive, " Treatise on Electricity" (Walker's translation), vol. i., p. 


explicitly uses the phrase, " a closed magnetic circuit." 
Joule 7 found the maximum power of an electromagnet 
to be proportional to " the least sectional area of the en- 
tire magnetic circuit," and he considered the resistance 
to induction as proportional to the length of the mag- 
netic circuit. Indeed, there are to be found scattered 
in Joule's writings on the subject of magnetism, some 
five or six sentences, which, if collected together, consti- 
tute a very full statement of the whole matter. Fara- 
day 8 considered that he had proved that each magnetic 
line of force constitutes a closed curve; that the path of 
these closed curves depended on the magnetic conduc- 
tivity of the masses disposed in proximity; that the 
lines of magnetic force were strictly analogous to the 
lines of electric flow in an electric circuit. He spoke of 
a magnet surrounded by air being like unto a voltaic 
battery immersed in water or other electrolyte. He 
even saw the existence of a power, analogous to that of 
electromotive force in electric circuits, though the name, 
" magneto-motive force/' is of more recent origin. The 
notion of magnetic conductivity is to be found in Max- 
well's great treatise (vol. ii., p. 51), but is only briefly 
mentioned. Rowland, 9 in 1873,- expressly adopted the 
reasoning and language of Faraday's method in the work- 
ing out of some new results on magnetic permeability, 
and pointed out that the flow of magnetic lines of force 

7 Ann. ofElectr., iv., 59, 1839; v., 195, 1841: and " Scientific Papers," pp. 8, 
31, 35, 36. 

8 " Experimental Researches, 11 vol. iii., art. 3117, 3228, 3230, 3260, 3271, 3276, 
3294, and 3361. 

Phil. Mag., series iv., vol. xlvi., Aug., 1873, ''On Magnetic Permeability 
and the Maximum of Magnetism of Iron, Steel, and Nickel. 1 ' 


through a bar could be subjected to exact calculation; 
the elementary law, he says, " is similar to the law of 
Ohm." According to Rowland, the " magnetizing force 
of helix " was to be divided by the " resistance to the 
lines of force;" a calculation for magnetic circuits 
which every electrician will recognize as precisely Ohm's 
law for electric circuits. He applied- the calculations 
to determine the permeability of certain specimens 
of iron, steel, and nickel. In 1882, 10 and again in 
1883, Mr. R. H. M. Bosanquet n brought out at greater 
length a similar argument, employing the extremely apt 
term " magneto-motive force " to connote the force tend- 
ing to drive the magnetic lines of induction through the 
" magnetic resistance," or, as it will frequently be called 
in these lectures, the magnetic "reluctance/ 7 of the cir- 
cuit. In these papers the calculations are reduced to a 
system, and deal not only with the specific properties of 
iron, but with problems arising out of the shape of the 
iron. Bosanquet shows how to calculate the several re- 
sistances (or reluctances) of the separate parts of the 
circuit, and then add them together to obtain the total 
resistance (or reluctance) of the magnetic circuit. 

Prior to this, however, the principle of the magnetic 
circuit had been seized upon by Lord Elphinstone and 
Mr. Vincent, who proposed to apply it in the construc- 
tion of dynamo-electric machines. On two occasions u 

10 Proc. Roy. Soc., xxxiv., p. 445, Dec., 1882. 

11 Phil Mag., series v., vol. xv., p. 205, Mar., 1883, "On Magneto-Motive 
Force." Also ib., vol. xix., Feb., 1885, and Proc. Roy. Soc., No. 223, 1883. 
See also The Electrician (London \ xiv., p. 291, Feb. 14, 1885. 

12 Proc. Roy. Soc., xxix., p. 292, 1879, and xxx., p. 287, 1880. See Electrical 
Review (London;, viii., p. 134, 1880. 


they communicated to the Royal Society the results of 
experiments to show that the same exciting current 
would evoke a larger amount of magnetism in a given 
iron structure, if that iron structure formed a closed 
magnetic circuit than if it were otherwise disposed. 

In recent years the notion of the magnetic circuit has 
been vigorously taken up by the designers of dynamo 
machines,, who, indeed, base the calculation of their de- 
signs upon this all-important principle. Having this, 
they need no laws of inverse squares of distances, no 
magnetic moments, none of the elaborate expressions for 
surface distribution of magnetism, none of the ancient 
paraphernalia of the last century. The simple law of 
the magnetic circuit and a knowledge of the properties 
of iron are practically all they need. About four years 
ago, much was done by Mr. Gisbert Kapp 13 and by Drs. 
J. and E. Hopkinson 14 in the application of these con- 
siderations to the design of dynamo machines, which 
previously had been a matter of empirical practice. To 
this end the formulae of Professor Forbes 15 for calculat- 
ing magnetic leakage, and the researches of Professors 
Ayrton and Perry 16 on magnetic shunts, contributed .a 
not unimportant share. As the result of the advances 
made at that time, the subject of dynamo design was 
reduced to an exact science. 

It is the aim and object of the present course of lec- 

13 The Electrician (London), vols. xiv., xv., and xvi., 1885-86; also Proc. 
Inst. Civil Engineers, Ixxxiii., 1885-86; and Jour. Soc. Telegr. Engineers, xv., 
524, 1886. 

14 Phil. Trans., 1886, pt. i., p. 331 ; and TJie Electrician (London), xviii., pp. 
39, 63, 86, 1886. 

15 Jour. Soc. Telegr. Engineers, xv., 555, 1886. 

16 Jour. Soc. Telegr. Engineers, xv., 530, 1886. 


tnres to show how the same considerations which have 
been applied with such great success to the subject of 
the design of dynamo-electric machines may be applied 
to the study of the electromagnet. The theory and 
practice of the design and construction of electromag- 
nets will thus be placed, once for all, upon a rational 
basis. Definite rules will be laid down for the guidance 
of the constructor, directing him as to the proper dimen- 
sions and form of iron to be chosen, and as to the proper 
size and amount of copper wire to be wound upon it in 
order to produce any desired result. 

First, however, a historical account of the invention 
will be given, followed by a number of general consid- 
erations respecting the uses and forms of electromag- 
nets. These will be followed by a discussion of the mag- 
netic properties of iron and steel and other materials; 
some account being added of the methods used for de- 
termining the magnetic permeability of various brands 
of iron at different degrees of saturation. Tabular in- 
formation is given as to the results found by different 
observers. In connection with the magnetic properties 
of iron, the phenomenon of magnetic hysteresis is also 
described and discussed. The principle of the magnetic 
circuit is then discussed with numerical examples, and 
a number of experimental data respecting the perform- 
ance of electromagnets are adduced, in particular those 
bearing upon the tractive power of electromagnets. The 
law of traction between an electromagnet and its arma- 
ture is then laid down, followed by the rules for pre- 
determining the iron cores and copper coils required to 
give any prescribed tractive force. 


Then comes the extension of the calculation of the 
magnetic circuit to those cases where there is an air-gap 
between the poles of the magnet and the armature, and 
where, in consequence, there is leakage of the magnetic 
lines from pole to pole. The rules for calculating the 
winding of the copper coils are stated, and the limiting 
relation between the magnetizing power of the coil and 
the heating effect of the current in it is explained. After 
this comes a detailed discussion of the special varieties 
of form that must be given to electromagnets in order 
to adapt them to special services. Those which are 
designed for maximum traction, for quickest action, for 
longest range, for greatest economy when used in con- 
tinuous daily service, for working in series with con- 
stant current, for use in parallel at constant pressure, 
and those for use with alternate currents are separately 

Lastly, some account is given of the various forms of 
electromagnetic mechanism which have arisen in con- 
nection with the invention of the electromagnet. The 
plunger and coil is specially considered as constituting 
a species of electromagnet adapted for a long range of 
motion. Modes of mechanically securing long range for 
electromagnets and of equalizing their pull over the 
range of motion of the armature are also described. 
The analogies between sundry electro-mechanical move- 
ments and the corresponding pieces of ordinary mech- 
anism are traced out. The course is concluded by a 
consideration of the various modes of preventing or 
minimizing the sparks which occur in the circuits in 
which electromagnets are used. 



The effect which an electric current, flowing in a wire, 
can exercise upon a neighboring compass needle was dis- 
covered by Oersted in 1820. 17 This first announcement 
of the possession of magnetic properties by an electric cur- 
rent was followed speedily by the researches of Ampere, 18 
Arago. 19 Davy, 20 and by the devices of several other ex- 
perimenters, including De La Rive's 21 floating battery 
and coil; Schweigger's 22 multiplier, Cumming's 23 gal- 
vanometer, Faraday's 24 apparatus for rotation of a per- 
manent magnet, Marsh's 25 vibrating pendulum, and 
Barlow's 26 rotating star-wheel. But it was not until 
1825 that the electromagnet was invented, Davy had, 
indeed, in 1821, surrounded with temporary coils of wire 
the steel needles upon which he was experimenting, and 
had shown that the flow of electricity around the coil 
could confer magnetic power upon the steel needles. 
But from this experiment it was a grand step forward 
to the discovery that a core of soft iron, surrounded by 
its own appropriate coil of copper, could be made to act 
not only as a powerful magnet, but as a magnet whose 
power could be turned on or off at will, could be aug- 

17 See Thomson's Annals of Philosophy, Oct., 1820. 
19 Ann. de Chim. et de Physique, xv., 59 and 170, 1820. 

19 /&., xv., 93, 1820. 

20 Phil. Trans., 1821. 

21 "BibliothequeUniverselle," Mar., 1821. 

i2 Ib. 23 camb. Phil. Trans., 1821. 

24 Quarterly Journal of Science, Sept., 1821. 

25 Barlow's " Magnetic Attractions," second edition, 1823. 
^ Ib. 


men ted to any desired degree, and could be set into 
action and controlled from a practically unlimited dis- 

The electromagnet, in the form which can first claim 
recognition for these qualities, was devised by William 
Sturgeon, 27 and is described by him in the paper which 
he contributed to the proceedings of the Society of Arts 
in 1825, accompanying a set of improved apparatus for 
electromagnetic experiments. 28 The Society of Arts 
rewarded Sturgeon's labors by awarding him the silver 
medal of the society and a premium of 30 guineas. 
Among this set of apparatus are two electromagnets, 

27 William Sturgeon, the inventor of the electromagnet, was born at Whit' 
tingtou, in Lancasln're, in 1783. Apprenticed as a boy to the trade of a shoe- 
maker, at the age of 19 he joined the Westmoreland militia, and two years 
later enlisted into the Royal Artillery, thus gaining the chance of learning 
something of science, and having leisure in which to pursue his absorbing 
passion for chemical and physical experiments. He was 42 ye:irsof age 
when he made his great, though at the time unrecognized, invention. At 
the date of his researches in electromagnetism he was resident at 8 Artillery 
place, Woolwich, at which place he was the associate of Marsh and was inti- 
mate with Barlow, Christie, and Gregory, who interested themselves in his 
work. In 1835 he presented a paper to the Royal Society containing descrip- 
tions, inter alia, of a magneto-electric machine with longitudinally wound 
armature, and with a commutator consisting of half discs of metal. For 
some reason this paper was not admitted to the Philosophical Transactions; 
he afterward printed it in full, without alteration, in his volume of ' Scien- 
tific Researches, 11 published by subscription in 1850. From 1836 to 1H43 he 
conducted the Annals of Electricity. He had now removed to Manchester, 
where he lectured on electricity at the Royal Victoria Gallery. He died at 
Prestwick, near Manchester, in 1850. There is a tablet to his menu >ry in the 
church atKirkby Lonsdale, from which town the village of Whittington is dis- 
tant about two miles. A portrait of Sturgeon in oils, and said to be an ex- 
cellent likeness, is believed still to be in existence; but all inquiries as to its 
whereabouts have proved unavailing. At the present moment, so far as I am 
aware, the scientific world is absolutely without a portrait of the inventor of 
the electromagnet. 

8 Trans. Society of Arts, 1825, xliii., p. 38 



one of horseshoe shape (Figs. 1 and 2) and one a straight 
bar (Fig. 3). It will be seen that the former figures 
present an electromagnet consisting of a bent iron rod 
about one foot long and a half inch in diameter, var- 
nished over and then coiled with a single left-handed 
spiral of stout uncovered copper wire of 18 turns. This 


coil was found appropriate to the particular battery 
which Sturgeon preferred, namely, a single cell contain- 
ing a spirally enrolled pair of zinc and copper plates of 
large area (about 130 square inches) immersed in acid; 
which cell, having small internal resistance, would yield 
a large quantity of current when connected to a circuit 
of small resistance. The ends of the copper wire were 
brought out sideways and bent down so as to dip in two 


deep connecting cups marked Z and (7, fixed upon a 
wooden stand. These cups, which were of wood, served 
as supports to hold up the electromagnet, and having 
mercury in them served also to make good electrical 
connection. In Fig. 2 the magnet is seen sideways, 
supporting a bar of iron, y. The circuit was completed 
to the battery through a connecting wire, d, which 
could be lifted out of the 
cup, Z, so breaking circuit 
when desired, and allowing 
the weight to drop. Stur- 
geon added in his explana- 
tory remarks that the poles, 
N and 8, of the magnet will 
be reversed if you wrap the 
copper wire about the rod as 
a right-handed screw, instead 
of a left-handed one, or, more 
simply, by reversing the con- 
nections with the battery, by 

Causing the wire that dips FIG. 3. STURGEON'S STRAIGHT-BAR 
into the Z CUp to dip into the ELECTROMAGNET. 

C cup, and vice versa. This electromagnet was capable 
of supporting nine pounds when thus excited. 

Fig. 3 shows another arrangement to fit on the same 
stand. This arrangement communicates magnetism to 
hardened steel bars as soon as they are put in, and ren- 
ders soft iron within it magnetic during the time of 
action; it only differs from Figs. 1 and 2 in being 
straight, and thereby allows the steel or iron bars to slide 
in and out. 


For this piece of apparatus and other adjuncts accom- 
panying it, all of which are described in the Society's 
Transactions for ]825, Sturgeon, as already stated, 
was awarded the society's silver medal and a premium 
of 30 guineas. The apparatus was deposited in the 
museum of the society, which therefore might be sup- 
posed to be the proud possessor of the first electromag- 
net ever constructed. Alas ! for the vanity of human 
affairs, the society's museum of apparatus has long been 
dispersed, this priceless relic having been either made 
over to the now defunct Patent-office Museum or other- 
wise lost sight of. 

Sturgeon's first electromagnet, the core of which 
weighed about seven ounces, was able to sustain a load 
of nine pounds, or about 20 times its own weight. At 
the time it was considered a truly remarkable perform- 
ance. Its single layer of stout copper wire was well 
adapted to the battery employed, a single cell of Stur- 
geon's own particular construction having a surface of 
130 square inches, and therefore of small internal resist- 
ance. Subsequently, in the hands of Joule, the same 
electromagnet sustained a load of 50 pounds, or about 
114 times its own weight. Writing in 1832 about his 
apparatus of 1825, Sturgeon used the following magnil- 
oquent language : 

"When first I showed that the magnetic energies of a 
galvanic conducting wire are more conspicuously exhibited 
by exercising them on soft iron than on hard steel, my ex 
pertinents were limited to small masses generally to a few 
inches of rod iron about half an inch in diameter. Some of 
those pieces were employed while straight, and others were 


bent into the form of a horseshoe magnet, each piece being 
compassed by a spiral conductor of copper wire. The mag- 
netic energies developed by these simple arrangements are 
of a very distinguished and exalted character, as is conspic- 
uously manifested by the suspension of a considerable 
weight at the poles during the period of excitation by the 
electric influence. 

"An unparalleled transiliency of magnetic action is also 
displayed in soft iron by an instantaneous transition from 
a state of total inactivity to that of vigorous polarity, and 
also by a simultaneous reciprocity of polarity in the ex- 
tremities of the bar versatilities in this branch of physics 
for the display of which soft iron is pre-eminently qualified, 
and which, by the agency of electricity, become demonstra- 
ble with the celerity of thought, and illustrated by experi- 
ments the most splendid in magnetics. It is, moreover, 
abundantly manifested by ample experiments, that gal- 
vanic electricity exercises a superlative degree of excitation 
on the latent magnetism of soft iron, and calls for its recon- 
dite powers with astonishing promptitude, to an intensity 
of action far surpassing anything which can be accom- 
plished by any known application of the most vigorous per- 
manent magnet, or by any other mode of experimenting 
hitherto discovered. It has been observed, however, by 
experimenting on different pieces selected from various 
sources, that, notwithstanding the greatest care be observed 
in preparing them of a uniform figure and dimensions, there 
appears a considerable difference in the susceptibility which 
they individually possess of developing the magnet powers, 
much of which depends upon the manner of treatment at 
the forge, as well as upon the natural character of the iron 
itself. 29 

29 " I have made a number of experiments on small pieces, from the re- 
sults of which it appears that much hammering is highly detrimental to the 
development of magnetism in soft iron, whether the exciting cause be gal- 
vanic or any other. And although good annealing is always essential and 
facilitates to a considerable extent the display of polarity, that process is 


"The superlative intensity of electromagnets, and the 
facility and promptitude with which their energies can be 
brought into play, are qualifications admirably adapted for 
their introduction into a variety of arrangements in which 
powerful magnets so essentially operate and perform a dis- 
tinguished part in the production of electromagnetic rota- 
tions ; while the versatilities of polarity of which they are 
susceptible are eminently calculated to give a pleasing di- 
versity in the exhibition of that highly interesting class of 
phenomena, and lead to the production of others inimita- 
ble by any other means." 30 

Sturgeon's further work during the next three years 
is best described in his own words : 

" It does not appear that any very extensive experiments 
were attempted to improve the lifting power of electromag- 
nets, from the time that my experiments were published in 
the Transactions of the Society of Arts, etc., for 1825, till 
the latter part of 1828. Mr. Watkins, philosophical instru- 
ment maker, Charing Cross, had, however, made them of 
much larger size than any which I had employed, but I am 
not aware to what extent he pursued the experiment. 

" In the year 1828, Professor Moll, of Utrecht, being on a 
visit to London, purchased of Mr. Watkins an electromag- 
net weighing about five pounds at that time, I believe, the 
largest which had been made. It was of round iron, about 
one inch in diameter, and furnished with a single copper 
wire twisted round it 83 times. When this magnet was ex- 
cited by a large galvanic surface, it supported about 75 
pounds. Professor Moll afterward prepared another electro- 
very far from restoring to the iron that degree of susceptibility which it fre- 
quently loses by the operation of the hammer. Cylindric rod iron of small 
dimensions may very easily be bent into the required form, without any ham- 
mering whatever; and I have found that small electromagnets made in this 
way display the magnetic powers in a very exalted degree/' 

30 Sturgeon's " Scientific Researches," p. 113. 


magnet, which, when bent, was 12-J inches high, 2i inches 
in diameter, and weighed about 26 pounds, prepared, like 
the former, with a single spiral conducting wire. With an 
acting galvanic surface of 11 square feet, this magnet would 
support 154 pounds, but would not lift an anvil which 
weighed 200 pounds. 

" The largest electromagnet which I have yet [1832] ex- 
hibited in my lectures weighs about 16 pounds. It is formed 
of a small bar of soft iron, 1| inches across each side ; the 
cross-piece which joins the poles is from the same rod of 
iron, arid about 3f inches long. Twenty separate strands 
of copper wire, each strand about 50 feet in length, are 
coiled around the iron, one above another, from pole to 
pole, and separated from each other by intervening cases 
of silk ; the first coil is only the thickness of one ply of silk 
from the iron; the twentieth, or outermost, about half an 
inch from it. By this means the wires are completely in- 
sulated from each other without the trouble of covering 
them with thread or varnish. The ends of wire project 
about two feet for the convenience of connection. With 
one of my small cylindrical batteries, exposing about 150 
square inches of total surface, this electromagnet supports 
400 pounds. I have tried it with a larger battery, but its 
energies do not seem to be so materially exalted as might 
have been expected by increasing the extent of galvanic 
surface. Much depends upon a proper acid solution ; good 
nitric or nitrous acid, with about six or eight times its quan- 
tity of water, answers very well. With a new battery of 
the above dimensions and a strong solution of salt and 
water, at a temperature of 190 degrees Fahr., the electro- 
magnet supported between 70 and 80 pounds when the first 
17 coils only were in the circuit. With the three exterior 
coils alone in the circuit, it would just support the lifter or 
cross-piece. When the temperature of the solution was be- 
tween 40 and 50 degrees, the magnetic force excited was 
comparatively very feeble. With the innermost coil alone 


and a strong acid solution this electromagnet supports 
about 100 pounds ; with the four outermost wires about 250 
pounds. It improves in power with every additional coil 
until about the twelfth, but not perceptibly any further; 
therefore the remaining eight coils appear to be useless, 
although the last three, independently of the innermost 17, 
and at the distance of half an inch from the iron, produce 
in it a lifting power of 75 pounds. 

" Mr. Marsh has fitted up a bar of iron much larger than 
mine with a similar distribution of the conducting wires to 
that devised and so successfully employed by Professor 
Henry. Mr. Marslfs electromagnet will support about 560 
pounds when excited by a galvanic battery similar to mine. 
These two, I believe, are the most powerful electromagnets 
yet produced in this country. 

"A small electromagnet, which I also employ on the lec- 
ture table, and the manner of its suspension, is represented 
by Fig. 3, Plate VI. The magnet is of cylindric rod iron 
and weighs four ounces ; its poles are about a quarter of an 
inch asunder. It is furnished with six coils of wire in the 
same manner as the large electromagnet before described, 
and will support upward of 50 pounds. 

" I find a triangular gin very convenient for the suspen- 
sion of the magnet in these experiments. A stage of thin 
board, supporting two wooden dishes, is fastened, at a 
proper height, to two of the legs of the gin. Mercury is 
placed in these vessels, and the dependent amalgamated 
extremities of the conducting wires dip into it one into 
each portion. 

" The vessels are sufficiently wide to admit of considerable 
motion of the wires in the mercury without interrupting 
the contact, which is sometimes occasioned by the swinging 
Of the magnet and attached weight. The circuit is com- 
pleted by other wires, which connect the battery with these 
two portions of mercury. When the weight is supported 
as in the figure, if an interruption be made by removing 


either of the connecting wires, the weight instantaneously 
drops on the table. The large magnet I suspend in the 
same way on a larger gin ; the weights which it supports 
are placed one after another on a square board, suspended 
by means of a cord at each corner from a hook in the cross- 
piece, which joins the poles of the magnet. 
" With a new battery and a solution of salt and water, at 


a temperature of 190 degrees Fahr., the small electromag- 
net, Fig. 3, Plate VI., supports 10 pounds." (See Fig. 4.) 

In 1840, after Sturgeon had removed to Manchester, 
where he assumed the management of the " Victoria 
Gallery of Practical Science," he continued his work, 
and in the seventh memoir in his series of researches he 
wrote as follows : 


" The electromagnet belonging to this institution is made 
of a cylindrical bar of soft iron, bent into the form of a 
horseshoe magnet, having the two branches parallel to each 
other arid at the distance of 4.5 inches. The diameter of the 
iron is 2.75 inches; it is 18 inches long when bent. It is sur- 
rounded by 14 coils of copper wire, seven on each branch. 
The wire which constitutes the coils is one-twelfth of an 
inch in diameter, and in each coil there are about 70 feet 
of wire. They are united in the usual way with branch 
wires, for the purpose of conducting the currents from the 
battery. The magnet was made by Mr. Nesbit. . . . The 
greatest weight sustained by the magnet in these experi- 
ments is 12f hundred-weight, or 1,386 pounds, which was 
accomplished by 16 pairs of plates, in four groups of four 
pairs in series each. The lifting power by 19 pairs in series 
was considerably less than by 10 pairs in series ; and but 
very little greater than that given by one cell or one pair 
only. This is somewhat remarkable, and shows how easily 
we may be led to waste the magnetic powers of batteries by 
an injudicious arrangement of its elements." 31 

At the date of Sturgeon's work the laws governing 
the flow of electric currents in wires were still obscure. 
Ohm's epoch-making enunciation of the law of the elec- 
tric circuit appeared in Poggendorff's Annalen in the 
very year of Sturgeon's discovery, 1825, though his 
complete book appeared only in 1827, and his work,, 
translated by Dr. Francis into English, only appeared 
(in Taylors "Scientific Memoirs/' vol. ii.) in 1841. 
Without the guidance of Ohm's law it was not strange 
that even the most able experimenters should not un- 
derstand the relations between battery and circuit which 
would give them the best effects. These had to be 

31 Sturgeon's "Scientific Researches," p. 188. 


found by the painful method of trial and failure. Pre*- 
eminent among those who tried was Prof. Joseph Henry, 
then of the Albany Institute in New York, later of 
Princeton, N. J., who succeeded in effecting an impor- 
tant improvement. In 1828, led on by a study of the 
" multiplier " (or galvanometer), he proposed to apply 
to electromagnetic apparatus the device of winding 
them with a spiral coil of wire " closely turned on it- 
self/' the wire being of copper from one-fortieth to one- 
twenty-fifth of an inch in diameter, covered with silk. 
In 1831 he thus describes 32 the results of his experi- 
ments : 

"A round piece of iron, about one-quarter of an inch in 
diameter, was bent into the usual form of a horseshoe, and 
instead of loosely coiling around it a few feet of wire, as is 
usually described, it was tightly wound with 35 feet of wire 
covered with silk, so as to form about 400 turns; a pair of 
small galvanic plates, which could be dipped into a tumbler 
of diluted acid, was soldered to the ends of the wire and 
the whole mounted on a stand. With these small plates 
the horseshoe became much more powerfully magnetic than 
another of the same size, and wound in the same manner, 
by the application of a battery composed of 28 plates of 
copper and zinc, each eight inches square. Another con- 
venient form of this apparatus was contrived by winding 
a straight bar of iron nine inches long with 35 feet of wire 
and supporting it horizontally on a small cup of copper 
containing a cylinder of zinc ; when this cup, which served 
the double purpose of a stand and the galvanic element, 
was filled with dilute acid the bar became a portable elec- 
tromagnet. These articles were exhibited to the institute 
in March, 1829. The idea afterward occurred to me that r, 

sa SillimarTs American Journal of Science, Jan., 1831, xix., p. 400. 


sufficient quantity of galvanism was furnished by the two 
small plates to develop, by means of the coil, a much greater 
magnetic power in a larger piece of iron. To test this, a 
cylindrical bar of iron, half an inch in diameter and about 
10 inches long, was bent into the shape of a horseshoe, ahd 
wound with 80 feet of wire ; with a pair of plates containing 
only 2| square inches of zinc it lifted 15 pounds avoirdupois. 
At the same time a very material improvement in the for- 
mation of the coil suggested itself to me on reading a more 
detailed account of Professor Schweigger's galvanometer, 
and which was also tested with complete success upon the 
same horseshoe; it consisted in using several strands of 
wire, each covered with silk, instead of one. Agreeably to 
this construction a second wire, of the same length as the 
first, was wound over it, and the ends soldered to the zinc 
and copper in such a manner that the galvanic current 
might circulate in the same direction in both, or in other 
words that the two wires might act as one ; the effect by 
this addition was doubled, as the horseshoe, with the same 
plates before used, now supported 28 pounds. 

" With a pair of plates four inches by six inches it lifted 
39 pounds, or more than 50 times its own weight. 

" These experiments conclusively proved that a great de- 
velopment of magnetism could be effected by a very small 
galvanic element, and also that the power of the coil Avas 
materially increased by multiplying the number of wires 
without increasing the number of each. 11 33 

Not content with these results, Professor Henry 
pushed forward on the line he had thus struck out. He 
was keenly desirous to ascertain how large a magnetic 
force lie could produce when using only currents of 
such a degree of smallness as could be transmitted 
through the comparatively thin copper wires, such as 

" "Scientific Writings of Joseph Henry, 11 p. 39. 


bell-hangers use. During the year 1830 he made great 
progress in this direction, as the following extracts show : 

" In order to determine to what extent the coil could be 
applied in developing magnetism in soft iron, and also to 
ascertain, if possible, the most proper length of the wires to 
be used, a series of experiments was instituted jointly by 
Dr. Philip Ten Eyck and myself. For this purpose 1,060 
feet (a little more than one-fifth of a mile) of copper wire 
of the kind called bell wire, .045 of an inch in diameter, 
were stretched several times across the large room of the 

" Experiment 1. A galvanic current from a single pair of 
plates of copper and zinc two inches square was passed 
through the whole length of the wire, and the effect on a 
galvanometer noted. From the mean of several observa- 
tions, the deflection of the needle was 15 degrees. 

" Experiment 2. A current from the same plates was 
passed through half the above length, or 530 feet of wire ; 
the deflection in this instance was 21 degrees. 

" By a reference to a trigonometrical table, it will be seen 
that the natural tangents of 15 degrees and 21 degrees are 
very nearly in the ratio of the square roots of 1 and 2, or of 
the relative lengths of the wires in these two experiments. 

" The length of the wire forming the galvanometer may 
be neglected, as it was only 8 feet long. 

" Experiment 3. The galvanometer was now removed, 
and the whole length of the wire attached to the ends of 
the wire of a small soft iron horseshoe, a quarter of an inch 
iri diameter, and wound with about eight feet of copper 
wire with a galvanic current from the plates used in expe- 
riments 1 and 2. The magnetism was scarcely observable 
in the horseshoe. 

"Experiment 4. The small plates were removed and a 
battery composed of a piece of zinc plate four inches by 
seven inches, surrounded with copper, was substituted. 


When this was attached immediately to the ends of the 
eight feet of wire wound round the horseshoe, the weight 
lifted was 4i pounds ; when the current was passed through 
the whole length of wire (1,060 feet) it lifted about half an 

" Experiment 5. The current was passed through half 
the length of wire (530 feet) with the same battery ; it then 
lifted two ounces. 

" Experiment 6. Two wires of the same length as in the 
last experiment were used, so as to form two strands from 
the zinc and copper of the battery ; in this case the weight 
lifted was four ounces. 

" Experiment 7. The whole length of the wire was at- 
tached to a small trough on Mr. Cruickshanks' plan, con- 
taining 25 double plates, and presenting exactly the same 
extent of zinc surface to the action of the acid as the battery 
used in the last experiment. The weight lifted in this case 
was eight ounces ; when the intervening wire was removed 
and the trough attached directly to the ends of the wire 
surrounding the horseshoe, it lifted only seven ounces. . . . 

" It is possible that the different states of the trough with 
respect to dryness may have exerted some influence on this 
remarkable result ; but that the effect of a current from a 
trough, if not increased, is but slightly diminished in pass- 
ing through a long wire is certain. . . . 

" But be this as it may, the fact that the magnetic action 
of a current from a trough is, at least, not sensibly dimin- 
ished by passing through a long wire is directly applicable 
to Mr. Barlow's project of forming an electromagnetic tele- 
graph ; and it is also of material consequence in the con- 
struction of the galvanic coil. From these experiments it is 
evident that in forming the coil we may either use one very 
long wire or several shorter ones, as the circumstances may 
require ; in the first case, our galvanic combinations must 
consist of a number of plates, so as to give ' projectile force ; ' 
in the second it must be formed of a single pair. 


" In order to test on a large scale the truth of these pre- 
liminary results, a bar of soft iron, two inches square and 
20 inches long, was bent into the form of a horseshoe 9| 
inches high. The sharp edges of the bar were first a little 
rounded by the hammer it weighed 21 pounds; a piece of 
iron from the same bar, weighing seven pounds, was filed 
perfectly flat on one surface, for an armature or lifter ; the 
extremities of the legs of the horseshoe were also truly 
ground to the surface of the armature ; around this horse- 
shoe 540 feet of copper bell wire were wound in nine coils of 
60 feet each; these coils were not continued around the 
whole length of the bar, but each strand of wire, according 
to the principle before mentioned, occupied about two 
inches, and was coiled several times backward and forward 
over itself; the several ends of the wires were left project- 
ing and all numbered, so that the first and last end of each 
strand might be readily distinguished. In this manner we 
formed an experimental magnet on a large scale, with which 
several combinations of wire could be made by merely unit- 
ing the different projecting ends. Thus if the second end 
of the first wire be soldered to the first end of the second 
wire, and so on through all the series, the whole will form 
a continuous coil of one long wire. 

"By soldering different ends the whole may be formed in 
a double coil of half the length, or into a triple coil of one- 
third the length, etc. The horseshoe was suspended in a 
strong rectangular wooden frame, 3 feet 9 inches high and 
20 inches wide; an iron bar was fixed below the magnet, so 
as to act as a lever of the second order ; the different weights 
supported were estimated by a sliding weight in the same 
manner as with a common steel-yard (see sketch). In the 
experiments immediately following (all weights being avoir- 
dupois) a small single battery was used, consisting of two 
concentric copper cylinders with zinc between them; the 
whol amount of zinc surface exposed to the acid from 
both sides of the zinc was two-fifths of a square foot; the 


battery required only half a pint of dilute acid for its sub- 

" Experiment 8. Each wire of the horseshoe \ soldered 
to the battery in succession, one at a time ; the agnetism 
developed by each was just sufficient to support the weight 
of the armature, weighing seven pounds. 

" Experiment 9. Two wires, one on each side of the arch 
of the horseshoe, were attached ; the weight lifted was 145 

" Experiment 10. With two wires, one from each extrem- 
ity of the legs, the weight lifted was 200 pound 

" Experiment 11. With three wires, one from each ex- 
tremity of the legs and one from the middle of the arch, 
the weight supported was 300 pounds. 

" Experiment 12. With four wires, two from each ex- 
tremity, the weight lifted was 500 pounds and the armature ; 
when the acid was removed from the zinc, the magnet con- 
tinued to support for a few minutes 130 pounds. 

" Experiment 13. With six wires the weight supported 
was 570 pounds; in all these experiments the wires were 
soldered to the galvanic element ; the connection in no case 
was formed with mercury. 

"Experiment^. When all the wires (nine in number) 
were attached, the maximum weight lifted was 650 pounds, 
and this astonishing result, it must be remembered, was 
produced by a battery containing only two-fifths of a square 
foot of zinc surface, and requiring only half a pint of dilute 
acid for its submersion. 

" Experiment 15. A small battery, formed with a plate 
of zinc 12 inches long and 6 inches wide, and surrounded by 
copper, was substituted for the galvanic elements used in the 
last experiment ; the weight lifted in this case was 750 pounds. 

" Experiment 16. In order to ascertain the effect of a 
very small galvanic elem'ent on this large quantity of iron, 
a pair of plates exactly one inch square was attached to all 
the wires ; the weight lifted was 85 pounds. 


" The following experiments were made with wires of dif- 
ferent lengths on the same horseshoe : 

" Experiment 17. With six wires, each 30 feet long, at- 
tached to the galvanic element, the weight lifted was 875 

" Experiment 18. The same wires used in the last experi- 
ment were united so as to form three coils of GO feet each; 
the weight supported was 290 pounds. This result agrees 
nearly with that of experiment 11, though the same indi- 
vidual wires were not used; from this it appears that six 
short wires are more powerful than three of double the 

' Experiment 19. The wires used in experiment 10, but 
united so as to form a single noil of 120 feet of wire, lifted 00 
pounds; while in experiment 10 the weight lifted was 200 
pounds. This is a confirmation of the result in the last ex- 
periment. . . . 

" In these experiments a fact was observed which appears 
somewhat surprising : when the large battery was attached, 
and the armature touching both poles of the magnet, it 
was capable of supporting more than 700 pounds, but when 
only one pole was in contact it did riot support more than 
five or six pounds, and in this case we never succeeded in 
making it lift the armature (weighing seven pounds). This 
fact may perhaps be common to all large magnets, but we 
have never seen the circumstance noticed of so great a dif- 
ference between a single pole and both. . . . 

"A series of experiments was separately instituted by Dr. 
Ten Eyck, in order to determine the maximum development 
of magnetism in a small quantity of soft iron. 

" Most of the results given in this paper were witnessed 
by Dr. L. C. Beck, and to this gentleman we are indebted 
for several suggestions, and particularly that of substitut- 
ing cotton well waxed for silk thread, which in these in- 
vestigations became a very considerable item of expense. 
He also made a number of experiments with iron bonnet 


wires, which, being found in commerce already wound, 
might possibly be substituted in place of copper. The re- 
sult was that with very short wire the effect was nearly the 
same as with copper, but in coils of long wire with a small 
galvanic element it was not found to answer. Dr. Beck 
also constructed a horseshoe of round iron one inch in 
diameter, with four coils on the plan before described. 
With one wire it lifted 30 pounds, with two wires 60 pounds, 
with three wires 85 pounds, and with four wires 112 pounds. 
While we were engaged in these investigations, the last 
number of the Edinburgh Journal of Science was received 
containing Professor Moll's paper on ' Electromagnetism.' 
Some of his results are in a degree similar to those here de- 
scribed ; his object, however, was different, it being only to 
induce strong magnetism on soft iron with a powerful gal- 
vanic battery. The principal object in these experiments 
was to produce the greatest magnetic force with the small- 
est quantity of galvanism. The only effect Professor Moll's 
paper has had over these investigations has been to hasten 
their publication; the principle on which they were insti- 
tuted was known to us nearly two years since, and at that 
time exhibited to the Albany Institute." 34 

In the next number of Silliman's Journal (April, 
1831) Professor Henry gave " an account of a large elec- 
tromagnet made for the laboratory of Yale College." 
The core of the armature weighed 59^ pounds; it was 
forged under Henry's own direction,, and wound "by Dr. 
Ten Eyck. This magnet, wound with 26 strands of 
copper bell wire of a total length of 728 feet, and excited 
by two cells which exposed nearly 4J square feet of sur- 
face, readily supported on its armature, which weighed 
23 pounds, a load of 2,063 pounds. 

34 " Scientific Writings of Joseph Henry, 11 p. 49. 


Writing in 1867 of his earlier experiments, Henry 


35 This figure, copied from the Scientific American, Dec. 11, 1880, represents 
Henry's electromagnet still preserved in Princeton College. The other appa- 
ratus at the foot, including a current-reverser, and the ribbon-coil used in the 
famous experiments on secondary and tertiary currents, were mostly con- 
structed by Henry's own hands. 


speaks 36 thus of his ideas respecting the use of addi- 
tional coils on the magnet and the increase of battery 

" To test these principles on a larger scale the experimen- 
tal magnet was constructed, which is shown in Fig. 6. In 
this a number of compound helices were placed on the same 
bar, their ends left projecting, and so numbered that they 
could all be united into one long helix, 
OT variously combined in sets of lesser 

" From a series of experiments with 
this and other magnets, it was proved 
that in order to produce the greatest 
amount of magnetism from a battery 
of a single cup a number of helices is 
required ; but when a compound bat- 
FIG. 6. HENRY'S Ex- tery is used then one long wire must 
ELECTRO " be employed, making many turns 
around the iron, the length of wire, 
and consequently the number of turns, being commensu- 
rate with the projectile power of the battery. 

" In describing the results of rny experiments, the terms 
'intensity' and .' quantity ' magnets were introduced to 
avoid circumlocution, and were intended to be used merely 
in a technical sense. By the intensity magnet I designated 
a piece of soft iron, so surrounded with wire that its mag- 
netic power could be called into operation by an intensity 
battery ; and by a quantity magnet, a piece of iron so sur- 
rounded by a number of separate coils that its magnetism 
could be fully developed by a quantity battery. 

" I was the first to point out this connection of the two 
kinds of the battery with the two forms of the magnet, in 

36 Statement in relation to the history of the electromagnetic telegraph, 
from the Smithsonian Annual Report for 1857, p. 99. 


my paper, in Si Hi marts Journal, January, 1831, and clearly 
to state that when magnetism was to be developed by 
means of a compound battery one long coil must be em- 
ployed, and when the maximum effect was to be produced 
by a single battery a number of single strands should be 
used. . . . Neither the electromagnet of Sturgeon nor any 
electromagnet ever made previous to my investigations 
was applicable to transmitting power to a distance. . . . 
The electromagnet made by Sturgeon and copied by Dana, 
of New York, was an imperfect quantity magnet, the feeble 
power of which was developed by a single battery. 1 ' 

Finally, Henry 37 sums up his own position as fol- 
lows : 

" 1. Previous to my investigations the means of develop- 
ing magnetism in soft iron were imperfectly understood, 
and the electromagnet which then existed was inapplicable 
to transmissions of power to a distance. 

" 2. I was the first to prove by actual experiment that in 
order to develop magnetic power at a distance a galvanic 
battery of ' intensity' must be employed to project the cur- 
rent through the long conductor, and that a magnet sur- 
rounded by many turns of one long wire must be used to 
receive this current. 

" 3. I was the first to actually magnetize a piece of iron at 
a distance, and to call attention to the fact of the applica- 
bility of my experiments to the telegraph. 

" 4. I was the first to actually sound a bell at a distance 
by means of the electromagnet. 

"5. The principles I had developed were applied by Dr. 
Grale to render Morse's machine effective at a distance." 

Though Henry's researches were published in 1831, 

s ' " Scientific Writings of Joseph Henry," vol. ii., p. 435. 


they were for some years almost unknown in Europe. 
Until April, 1837, when Henry himself visited Wheat- 
stone at his laboratory at King's College, the latter did 
not know how to construct an electromagnet that could 
be worked through a long wire circuit. Cooke, who 
became the coadjutor of Wheatstone, had originally 
come to him to consult him, 38 in February, 1837, about 
his telegraph and alarum, the electromagnets of which, 
though they worked well on short circuits, refused to 
work when placed in circuit with even a single mile of 
wire. Wheats tone's own account 39 of the matter is 
extremely explicit : " Relying on my former experience, 
I at once told Mr. Cooke that his plan would not and 
could not act as a telegraph, because sufficient attractive 
power could not be imparted to an electromagnet inter- 
posed in a long circuit; and, to convince him of the 
truth of this assertion, I invited him to King's College 
to see the repetition of the experiments on which my 
conclusion was founded. He came, and after seeing a 
variety of voltaic magnets, which even with powerful 
batteries exhibited only slight adhesive traction, he 
expressed his disappointment." 

After Henry's visit to Wheatstone, the latter altered 
his tone. He had been using, faute de mieux, relay cir- 
cuits to work the electromagnets of his alarum in a 
short circuit with a local battery. "These short cir- 
cuits," he writes, "have lost nearly all their importance 

38 See Mr. Latimer Clark's account of Cooke in vol. viii. of Jour. Soc. 
Telegr. Engineers, p. 374. 1880. 

39 W. F. Cooke, "The Electric Telegraph ; Was it Invented by Prof. Wheat- 
stone?" 1856-57, part ii., p. 87. 


and are scarcely worth contending about since my dis- 
covery " (the italics are our own) " that electromagnets 
may be so constructed as to produce the required effects 
by means of the direct current, even in very long cir- 
cuits." 40 

We pass on to the researches of the distinguished 
physicist of Manchester, whose decease we have lately 
had to deplore, Mr. James Prescott Joule, who, fired by 
the work of Sturgeon, made most valuable contributions 
to the subject. Most of these were published either in 
Sturgeon's Annals of Electricity, or in the Proceedings 
of the Literary and Philosophical Society of Manchester, 
but their most accessible form is the republished vol- 
ume issued five years ago by the Physical Society of 

In his earliest investigations he was endeavoring to 
work out the details of an electric motor. The follow- 
ing is an extract from his own account (" Reprint of 
Scientific Papers," p. 7) : 

" In the further prosecution of my inquiries, I took six 
pieces of round bar iron of different diameters and lengths, 
also a hollow cylinder, one -thirteenth of an inch thick in 
the metal. These were bent in the U-form, so that the 
shortest distance between the poles of each was half an 
inch ; each was then wound with 10 feet of covered copper 
wire, one-fortieth of an inch in diameter. Their attractive 
powers under like currents for a straight steel magnet, 1 
inches long, suspended horizontally to the beam of a bal- 
ance, were, at the distance of half an inch, as follows : (See 
table on page 40. ) 

"A steel magnet gave an attractive power of 23 grains, 
while its lifting power was not greater than 00 ounces. 

Ib., p. 95. 





















Length round the bend in 
inches. . 
Diameter in inches 
Attraction for steel magnet, in 
Weight lifted, in ounces 














" The above results will not appear surprising if we 
consider, first, the resistance which iron presents to the 
induction of magnetism, and, second, how very much the 
induction is exalted by the completion of the magnetic 

" Nothing can be more striking than the difference be- 
tween the ratios of lifting to attractive power at a distance 
in the different magnets. While the steel magnet attracts 
with a force of 23 grains and lifts 60 ounces, the electromag- 
net No. 3 attracts with a force of only 5.1 grains, but lifts 
as much as 92 ounces. 

" To make a good electromagnet for lifting purposes . 1st. 
Its iron, if of considerable bulk, should be compound, of 
good quality, and well annealed. 3d. The bulk of the iron 
should bear a much greater ratio to its length than is gen- 
erally the case. 3d. The poles should be ground quite true, 
arid fit flatly and accurately to the armature. 4th. The 
armature should be equal in thicknesi to the iron of the 

" In studying what form of electromagnet is best for at- 
traction from a distance, two things must be considered, 
viz., the length of the iron and its sectional area. 

" Now I have always found it disadvantageous to increase 
the length beyond what is needful for the winding of the 
covered wire. 1 ' 

These results were announced in March, 1839. In 
May of the same year he propounded a law of the mutual 


attraction of two electromagnets as follows: "The at- 
tractive force of two electromagnets for one another is 
directly proportional to the square of the electric force 
to which the iron is exposed; or if j? denote the elec- 
tric current, TFthe length of wire, and M the magnetic 
attraction, M=E*W*" The discrepancies which he 
himself observed he rightly attributed to the iron be- 
coming saturated magnetically. In March, 1840, he ex- 


tended this same law to the lifting power of the horse- 
shoe electromagnet. 

In August, 1840, he wrote to i\\Q Annals of Electricity 
on electromagnetic forces, dealing chiefly with some 
special electromagnets for traction. One of these pos- 
sessed the form shown in Fig. 7. Both the magnet and 
the iron keeper were furnished with eye-holes for the 
purpose of suspension and measurement of the force 
requisite to detach the keeper. Joule thus writes about 
the experiments : 41 

" I proceed now to describe my electromagnets, which I 
constructed of very different sizes in order to develop any 

41 " Scientific Papers, 11 vol. i., p. 30. 


curious circumstance which might present itself. A piece 
of cylindrical wrought iron, eight inches long, had a hole 
one inch in diameter bored the whole length of its axis, 
one side was planed until the hole was exposed sufficiently 
to separate the thus formed poles one-third of an inch. 
Another piece of iron, also eight inches long, was then 
planed, and, being secured with its face in contact with the 
other planed surface, the whole was turned into a cylinder 
eight inches long, 3f inches in exterior, and one inch interior 
diameter. The larger piece was then covered with calico 
and wound with four copper wires covered with silk, each 
23 feet long and one-eleventh of an inch in diameter a 
quantity just sufficient to hide the exterior surface, and to 
fill the interior opened hole. . . . The above is designated 
No. 1 ; and the rest are numbered in tha order of their de- 

" I made No. 2 of a bar of half- inch round iron 2. 7 inches 
long. It was bent into an almost semicircular shape and 
then covered with seven feet of insulated copper wire ^ inch 
thick. The poles are half an inch asunder, and the wire 
completely fills the space between them. 

"A third electromagnet was made of a piece of iron 0. 7 
inch long, 0.37 inch broad, and 0.15 inch thick. Its edges 
were reduced to such an extent that the transverse section 
was elliptical. It was bent into a semicircular shape, and 
wound with 19 inches of silked copper wire fa inch in diam- 

" To procure a still more extensive variety, I constructed 
what might, from its extreme minuteness, be termed an ele- 
mentary electromagnet. It is the smallest, I believe, ever 
made, consisting of a bit of iron wire \ inch long and fa inch 
in diameter. It was bent into the shape of a semicircle, 
and was wound with three turns of uninsulated copper wire 
fa inch in thickness." 

With these magnets experiments were made with vari- 


ous strengths of currents, the tractive forces being 
measured by an arrangement of levers. The results, 
briefly, are as follows : Electromagnet No. 1, the iron 
of which weighed ] 5 pounds, required a weight of 2,090 
pounds to detach the keeper. No. 2, the iron of which 
weighed 1,057 grains, required 49 pounds to detach its 
armature. No. 8, the iron of which weighed 65.3 grains, 
supported a load of 12 pounds, or 1,280 times its own 
weight. No. 4, the weight of which was only half a 
grain, carried in one instance 1,41 7 grains, or 2,834 times 
its own weight. 

" It required much patience to work with an arrangement 
so minute as this last ; and it is probable that I might ulti- 
mately have obtained a larger figure than the above, which, 
however, exhibits a power proportioned to its weight far 
greater than any on record, and is eleven times that of the 
celebrated steel magnet which belonged to Sir Isaac New- 

" It is well known that a steel magnet ought to have a 
much greater length than breadth or thickness; and Mr. 
Scoresby has found that when a large number of straight 
steel magnets are bundled together, the power of each when 
separated and examined is greatly deteriorated. All this is 
easily understood, and finds its cause in the attempt of each 
part of the system to induce upon the other part a contrary 
magnetism to its own. Still there is no reason why the 
principle should in all cases be extended from the steel to 
-the electromagnet, since in the latter case a great and com- 
manding inductive power is brought into play to sustain 
what the former has to support by its own unassisted re- 
tentive property. All the preceding experiments support 
this position; and the following table gives proof of the 
obvious and necessary general consequence: the maximum 
power of the electromagnet is directly proportional to its 



least transverse sectional area. The second column of the 
table contains the least sectional area in square inches of 
the entire magnetic circuit. The maximum power in pounds 
avoirdupois is recorded in the third; and this, reduced to 
an inch square of sectional area, is given in the fourth col- 
umn under the title of specific power. 






f Xo. 1 
My own electromagnets ' ^' | ' ' 

[NO! '4. '.'.'.'..'..'..'.'".'.'.'.'. 

Mr. J. C. Nesbit's.- Length round the curve, 3 
feet ; diameterof iron core, 2% inches : sectional 
area, 5.7 inches; do. of armature, 4.5 inches; 
\\ eight of iron, about 50 pounds 


4 5 


1 48 





Prof. Henry's. Lengi h round the curve. 20 inches ; 
section, 2 inches square; sharp edges i ounded 
off ; weight, 21 pounds 
Mr. Sturg on's original. Length round the curve, 
about 1 foot ; diameter of the round bar, y 2 i'^-'h 




" The above examples are, I think, sufficient to prove the 
rule I have advanced. No. 1 was probably not fully satu- 
rated ; otherwise I have no doubt that its power per jj^uare 
inch would have approached 800. Also the specific power 
of No. 4 is small, because of the difficulty of making a good 
experiment with it." 

These experiments were followed by some to ascertain 
the effect of the length of the iron of the magnet, whicl 
he considered, at least in those cases where the degree 
of magnetization is considerably below the point of 
saturation, to offer a decidedly proportional resistance 
to magnetization; a view the justice of which is now, 
after 50 years, amply confirmed. 


In November of the same year further experiments 42 
in the same direction were published. A tube of iron, 
spirally made and welded, was prepared, planed down 
as in the preceding case, and fitted to a similarly pre- 
pared armature. The hollow cylinder thus formed, 
shown in Fig. 8, was two feet in length. Its external 
diameter was 1.42 inches, its internal being 0.5 inch. 
The least sectional area was 10^ square inches. The 
exciting coil consisted of a single copper rod, covered 
with tape, bent into a sort of S-shape. This was later 
replaced by a coil of 21 copper wires, each ^ inch in 


diameter and 23 feet long, bound together by cotton 
tape. This magnet, excited by a battery of 1C of Stur- 
geon's cast-iron cells, each one foot square and one and 
a half inches in interior width, arranged in a series of 
four, gave a lifting power of 2,775 pounds. 

Joule's work was well worthy of the master from 
whom he had learned his first lesson in electromagnet- 
ism. He showed his devotion not only by writing de- 
&criptions of them for Sturgeon's Annals, but by exhib- 
iting two of his electromagnets at the Victoria Gallery 
of Practical Science, of which Sturgeon was director. 
Others, stimulated into activity by Joule's example, pro- 
posed new forms, among them being two Manchester 

<a "Scientific Papers," p. 40, and Annals of Electricity, vol. v., p. 170. 



gentlemen, Mr. Radford and Mr. Richard Roberts, the 
latter being a well-known engineer and inventor. Mr. 
^ Radford's electromagnet consisted 

^P of a flat iron disc with deep spiral 

grooves cut in its face, in which 
were laid the insulated copper wires. 
The armature consisted of a plain 
iron disc of similar size. This form 
is described in Vol. IV. of Sturgeon's 



Mr. Roberts' form of electro- 
magnet consisted of a rectangular 
ELEC- j ron block, having straight parallel 
grooves cut across its face, as in Fig. 
9. This was described in Vol. VI. of Sturgeon's An- 
nals, page 166. Its face was 6-f inches square and 
its thickness 2 T V inches. It 
weighed, with the conducting 
wire, 35 pounds; and the arm- 
ature, of the same size and 
1| inches thick, weighed 23 
pounds. The load sustained 
by this magnet was no less 
than 2,950 pounds. Roberts 
inferred that a magnet if made 
of equal thickness, but five 

feet Square, Would Sustain 100 FlG " 10.-JouLB's ZIGZAG ELEC- 

tons' weight. Some of Roberts' 

apparatus is still preserved in the Museum of Peel 

Park, Manchester. 

On page 431 of the same volume of the Annals Joule 


described yet another form of electromagnet, the form 
of which resembled in general Fig. 10, but which, in 
actual fact, was built up of 24 separate flat pieces of iron 
bolted to a circular brass ring. The armature was a 
similar structure, but not wound with wire. The iron 
of the magnet weighed seven pounds and that of the 
armature 4.55 pounds. The weight lifted was 2,710 
pounds when excited by 16 of Sturgeon's cast-iron cells. 

In a subsequent paper on the calorific effects of mag- 
neto-electricity, 43 published in 1843, Joule described 
another form of electromagnet of horseshoe shape, made 
from a piece of boiler-plate. This was not intended to 
give great lifting power, and was used as the field mag- 
net of a motor. In 1852 another powerful electromag- 
net of horseshoe form, somewhat similar to the preced- 
ing, was constructed by Joule for experiment. He came 
to the conclusion 44 that, owing to magnetic saturation 
setting in, it was improbable that any force of electric 
current could give a magnetic attraction greater than 
200 pounds per square inch. " That is, the greatest 
weight which could be lifted by an electromagnet formed 
of a bar of iron one inch square, bent into a semicircu- 
lar shape, would not exceed 400 pounds." 

With the researches of Joule may be said to end the 
first stage of development. The notion of the magnetic 
circuit which had thus guided Joule's work did not 
commend itself at that time to the professors of physi- 
cal theories; and the practical men, the telegraph en- 

43 "Scientific Papers," vol. i., p. 1523; and Phil. Mag., ser. iii., vol. xxiii., p. 
863, 1843. 
" Scientific Papers, 1 ' vol. i., p. 362; and Phil. Mag., ser. iv., vol. iii., p. 32. 


gineers, were for the most part content to work by 
purely empirical methods. Between the practical man 
and the theoretical man there was, at least on this topic, 
a great gulf fixed. The theoretical man, arguing as 
though magnetism consisted in a surface distribution of 
polarity, and as though the laws of electromagnets were 
like those of steel magnets, laid down rules not applica- 
ble to the cases which occur in practice, and which 
hindered rather than helped progress. The practical 
man, finding no help from theory, threw it on one side 
as misleading and useless. It is true that a few work- 
ers made careful observations and formulated into rules 
the results of their investigations. Among these, the 
principal were Ritchie,, Robinson, Muller, Dub, Von 
Koike, and Du Moncel; but their work was little known 
beyond the pages of the scientific journals wherein their 
results were described. Some of these results will be 
examined in my later lectures, but they cannot be dis- 
cussed in this historical resume, which is accordingly 


Materials. In any complete treatise on the electro- 
magnet it would be needful to enumerate and to discuss 
in detail the several constructive features of the ap- 
paratus. Three classes of material enter into its con- 
struction : first, the iron which constitutes the material 
of the magnetic circuit, including the armature as well 
as the cores on which the coils are wound, and the yoke 
that connects them; secondly, the copper which is em- 
ployed as the material to conduct the electric cur- 


rents, and which is usually in the form of wire; thirdly, 
the insulating material employed to prevent the copper 
coils from coming into contact with one another, or 
with the iron core. There is a further subject for dis- 
cussion in the bobbins, formers, or frames upon which 
the coils are in so many cases wound, and which may in 
some cases be made in metal, but often are not. The 
engineering of the electromagnet might well furnish 
matter for a special chapter. 


It is difficult to devise a satisfactory or exhaustive 
classification of the varied forms which the electromag- 
net has assumed, but it is at least possible to enumerate 
some of the typical forms. 

1. Bar Electromagnet. This consists of a single 
straight core (whether solid, tubular, or laminated), sur- 
rounded by a coil. Fig. 3 depicted Sturgeon's earliest 

2. Horseshoe Electromagnet. There are two sub-types 
included in this name. The original electromagnet of 
Sturgeon (Fig. 1) really resembled a horseshoe in form, 
being constructed of a single piece of round wrought 
iron, about half an inch in diameter and nearly a 
foot long, bent into an arch. In recent years the other 
sub-type has prevailed, consisting, as shown in Fig. 11, 
of two separate iron cores, usually cut from a circular 
rod, fixed into a third piece of wrought iron, the yoke. 
Occasionally this form is modified by the use of one coil 
only, the second co v e being left uncovered. This form 
has received in France the name of aimant Mteux, Its 




merits will be considered later. Sometimes a single coil 
is wound upon the yoke, the two limbs being uncovered. 


3. Iron-clad Electromagnet. This form, which has 
many times been re-invented, differs from the simple 
bar magnet in having an iron shell 
or casing external to the coils and 
attached to the core at one end. 
Such a magnet presents, as de- 
picted in Fig. 12, a central pole at 
one end surrounded by an outer 
annular pole of the opposite polar- 
ity. The appropriate armature for 
electromagnets of this type is a cir- 
cular disc or lid of iron. 
FIG. 12. -IRON-CLAD ELEC- 4. Coil-and-Plunger. A de- 


tached iron core is attracted into 
a. hollow coil, or solenoid, of copper wire, when a om*- 


rent of electricity flows round the latter. This is a 
special form, and will receive extended consideration. 

5. Special Forms. Besides the leading forms enumer- 
ated above, there are a number of special types, multi- 
polar, spiral, and others designed for particular pur- 
poses. There is also a group of forms intermediate 
between the ordinary electromagnet and the coil-and- 
plunger form. 


It is a familiar fact that the polarity of an electro- 
magnet depends upon the sense in which the current 
is flowing around it. Various rules for remembering 


the relation of the electric flow and the magnetic force 
have been given. One of them that is useful is that 
when one is looking at the north pole of an electromag- 
net, the current will be flowing around that pole in the 
sense opposite to that in which the hands of a clock are 


seen to revolve. Another useful rule, suggested by Max- 
well, is illustrated by Fig. 13, namely, that the sense of 
the circulation of the current (whether right or left 
handed) and the positive direction of the resulting mag- 
netic force are related together in the same way as the 
rotation and the travel of a right-handed screw are as- 
sociated together. Right-handed rotation of the screw 
is associated with forward travel. Right-handed circu- 
lation of a current is associated with a magnetic force 
tending to produce north polarity at the forward end 
of the core. 


As a piece of mechanism an electromagnet may be 
regarded as an apparatus for producing a mechanical 
action at a place distant from the operator who controls 
it, the means of communication from the operator to 
the distant point where the electromagnet is being the 
electric wire. The uses of electromagnets may, how- 
ever, be divided into two main divisions. For certain 
purposes an electromagnet is required merely for ob- 
taining temporary adhesion or lifting power. It at- 
taches itself to an armature and cannot be detached so 
long as. the exciting current is maintained, except by 
the application of a superior opposing pull. The force 
which an electromagnet thus exerts upon an armature 
of iron, with which it is in direct contact, is always con- 
siderably greater than the force with which it can act 
on an armature at some distance away, and the two 
cases must be carefully distinguished. Traction of an 
armature in contact and attraction of an armature at a. 


distance are two different functions. So different, in- 
deed, that it is no exaggeration to say that an electro- 
magnet designed for the one purpose is unfitted for the 
other. The question of designing electromagnets for 
either of these purposes will occupy a large part of 
these lectures. The action which an electromagnet ex- 
ercises on an armature in its neighborhood may be of 
several kinds. If the armature is of soft iron, placed 
nearly parallel to the polar surfaces, the action is one 
simply of attraction, producing a motion of pure trans- 
lation, irrespective of the polarity of the magnet. If 
the armature lies oblique to the lines of the poles there 
will be a tendency to turn it round, as well as to attract 
it; but, again, if the armature is of soft iron the action 
will be independent of the polarity of the magnet, that 
is to say, independent of the direction of the exciting 
current. If, however, the armature be itself a magnet 
of steel permanently magnetized, then the direction in 
which it tends to turn, and the amount, or even the 
sign of th force with which it is attracted, will depend 
on the polarity of the electromagnet; that is to say, will 
depend on the direction in which the exciting current 
circulates. Hence there arises a difference between the 
operation of a non-polarized and that of a polarized ap- 
paratus, the latter term being applied to those forms in 
which there is employed a portion say an armature 
to which an initial fixed magnetization has been im- 
parted. Non-polarized apparatus is in all cases inde- 
pendent of the direction of the current. Another class 
of uses served by electromagnets is the production of 
rapid vibrations. These are employed in the median- 


ism of electric trembling bells, in the automatic breaks 
of induction coils, in electrically driven tuning-forks 
such as are employed for chronographic purposes, and 
in the instruments used in harmonic telegraphy. Spe- 
cial constructions of electromagnets are appropriate to 
special purposes such as these. The adaptation of elec- 
tromagnets for the special end of responding to rapidly 
alternating currents is a closely kindred matter. Lastly, 
there are certain applications of the electromagnet, no- 
tably in the construction of some forms of arc lamp, for 
which it is specially sought to obtain an equal, or ap- 
proximately equal, pull over a definite range of motion. 
This use necessitates special designs. 


A knowledge of the magnetic properties of iron of 
different kinds is absolutely fundamental to the theory 
and design of electromagnets. No excuse is therefore 
necessary for treating this matter with some fullness. 
In all modern treatises on magnetism the usual terms 
are defined and explained. Magnetism, which was 
formerly treated of as though it were something distrib- 
uted over the end surfaces of magnets, is now known 
to be a phenomenon of internal structure; and the ap 
propriate mode of considering it is to treat the mag- 
netic materials, iron and the like, as being capable of 
acting as good conductors of the magnetic lines; in 
other words, as possessing magnetic permeability. The 
precise notion now attached to this word is that of a 
numerical coefficient. Suppose a magnetic force due, 
let us say, to the circulation of an electric current in a 


surrounding coil were to act on a space occupied by 
air: there would result a certain number of magnetic 
lines in that space. In fact, the intensity of the mag- 
netic force, symbolized by the letter H, is often ex- 
pressed by saying that it would produce H magnetic 
lines per square centimetre in air. Now, owing to the 
superior magnetic power of iron, if the space subjected 
to this magnetic force were filled with iron instead of 
air, there would be produced a larger number of mag- 
netic lines per square centimetre. This larger number 
in the iron expresses the degree of magnetization in the 
iron; it is symbolized 45 by the letter B. The ratio of 
B and H expresses the permeability of the material. 
The usual symbol for permeability is the Greek letter /*. 
So we may say that B is equal to P. times H. For ex- 
ample, a certain specimen of iron when subjected to a 
magnetic force capable of creating, in air, 50 magnetic 
lines to the square centimetre, was found to be perme- 
ated by no fewer than 16,062 magnetic lines per square 

45 The following are the various ways of expressing the three quantities 
under consideration: 

B The internal magnetization. 
The magnetic induction. 
The induction. 

The intensity of the induction. 
The permeation. 

The number of lines per square centimetre in the material. 
H The magnetizing force at a point. 
The magnetic force at a point. 
The intensity of the magnetic force. 

The number of lines per square centimetre that there would be in air. 
M The magnetic permeability. 
The permeability. 

The specific conductivity for magnetic lines. 
The magnetic multiplying power of the material. 


centimetre. Dividing the latter figure by the former 
gives as the value of the permeability at this stage of 
the magnetization 321, or the permeability of the iron 
is 321 times that of air. The permeability of such non- 
magnetic materials as silk, cotton, and other insulators, 
also of brass, copper, and all the non-magnetic metals, is 
taken as 1, being practically the same as that of the air. 
This mode of expressing the fact is, however, compli- 
cated by the fact of the tendency in all kinds "of iron to 
magnetic saturation. In all kinds of iron the magneti- 
zability of the material becomes diminished as the actual 
magnetization is pushed further. In other words, when 
a piece of iron has been magnetized up to a certain 
degree it becomes, from that degree onward, less perme- 
able to further magnetization, and though actual satu- 
ration is never reached, there is a practical limit beyond 
which the magnetization cannot well be pushed. Joule 
was one of the first to establish this tendency toward 
magnetic saturation. Modern researches have shown 
numerically how the permeability diminishes as the 
magnetization is pushed to higher stages. The practi- 
cal limit of the magnetization, B, in good wrought iron 
is about 20,000 magnetic lines to the square centimetre, 
or about 125,000 lines to the square inch; and in cast 
iron the practical saturation limit is nearly 12,000 lines 
per square centimetre, or about 70,000 lines per square 
inch. In designing electromagnets, before calculations 
can be made as to the size of a piece of iron required 
for the core -of a magnet for any particular purpose, it 
is necessary to know the magnetic properties of that 
piece of iron; for it is obvious that if the iron be of in- 


ferior magnetic permeability, a larger piece of it will be 
required in order to produce the same magnetic effect 
as might be produced with a smaller piece of higher 
permeability. Or, again, the piece having inferior per- 
meability will require to have more copper wire wound 
on it; for in order to bring up its magnetization to the 
required point, it must be subjected to higher magnetiz- 

L> 10 20 30 40 50 


ing forces than would be necessary if a piece of higher 
permeability had been selected. 

A convenient mode of studying the magnetic facts 
respecting any particular brand of iron is to plot on a 
diagram the curve of magnetization i. e., the curve in 
which the values, plotted horizontally, represent the 
magnetic force H, and the values plotted vertically those 
that correspond to the respective magnetization B. In 
Fig. 14, which is modified from the researches of Prof. 


Ewing, are given five curves relating to soft iron, 
hardened iron, annealed steel, hard drawn steel, and 
glass-hard steel. It will be noticed that all these curves 
have the same general form. For small values of H the 
values of B are small, and as H is increased B increases 
also. Further, the curve rises very suddenly, at least 
with all the softer sorts of iron, and then bends over and 
becomes nearly horizontal. When the magnetization 
is in the stage below the bend of the curve, the iron is 
said to be far from the state of saturation. But when 
the magnetization has been pushed beyond the bend of 
the curve, the iron is said to be in the stage approach- 
ing saturation; because at this stage of magnetization 
it requires a large increase in the magnetizing force to 
produce even a very small increase in the magnetization. 
It will be noted that for soft wrought iron the stage of 
approaching saturation sets in when B has attained the 
value of about 16,000 lines per square centimetre, or 
when H has been raised to the value of about 50. As 
we shall see, it is not economical to push B beyond this 
limit; or, in other words, it does not pay to use stronger 
magnetic forces than those of about H 50. 


There are four sorts of experimental methods of 
measuring permeability. 

1. Magnetometric Methods. These are due to Miiller, 
and consist in surrounding a bar of the iron in question 
by a magnetizing coil and observing the deflection its 
magnetization produces in a rhagnetometer. ' 

2. Balance Methods. These methods are a variety of 


the preceding, a compensating magnet being employed 
to balance the effect produced by the magnetized iron 
on the magnetometric needle. Von Feilitzsch used this 
method, and it has received a more definite applica-. 
tion in the magnetic balance of Prof. Hughes. The 
actual balance is exhibited to-night upon the table, and 
I have beside me a large number of observations made 
by students of the Finsbury Technical College by its 
means upon sundry samples of iron and steel. None 
of these methods are, however, to be compared with 
those that follow. 

3. Inductive Methods. There are several varieties of 
these, but all depend on the generation of a transient 
induction current in an exploring coil which surrounds 
the specimen of iron, the integral current being propor- 
tional to the number of magnetic lines introduced into, 
or withdrawn from, the circuit of the exploring coil. 
Three varieties may be mentioned. 

(A) Ring Method. In this method, due to Kirch- 
hoff, the iron under examination is made up into a ring, 
which is wound with a primary or exciting coil arid 
with a secondary or exploring coil. Determinations on 
this plan have been made by Stowletow, Rowland, Bosan- 
quet, and Ewing; also by Hopkinson. Rowland's ar- 
rangement of the experiment is shown in Fig. 15 in 
which B is the exciting battery; #, the switch for turn- 
ing on or reversing the current; J?, an adjustable resist- 
ance; A, an amperemeter; and B G the ballistic galva- 
nometer, the first swing of which measures the integral 
induced current. R C is an earth inductor or reversing 
coil wherewith to calibrate the readings of the galva- 



nometer; and above is an arrangement of a coil and a 
magnet to assist in bringing tbe swinging needle to rest 
between the observations. The exciting coil and the 
exploring coil are both wound upon the ring: the former 
is distinguished by being drawn with a thicker line. 
The usual mode of procedure is to begin with a feeble 
exciting current, which is suddenly reversed, and then 
reversed back. The current is then increased, reversed 


and re-reversed; and so on, until the strongest available 
points are reached. The values of the magnetizing 
force H are calculated from the observed value of the 
current by the following rule. If the strength of the 
current, as measured by the amperemeter, be t, the num- 
ber of spires of the exciting coil S and the length, in 
centimetres, of the coil (i. e., the mean circumference of 
the ring) be /, then H is given by the formula: 

4- .Si Si 

H = -- X -j- = 1.2566 X -- 



Bosanquet, applying this method to a number of iron 
rings, obtained some important results. 

In Fig. 16 are plotted out the values of H and B for 
seven rings. One of these, marked /, was of cast steel, 
and was examined both when soft and afterward when 
hardened. Another, marked /, was of the best Lowrnoor 
iron. Five were of Crown iron, of different sizes. They 
were marked for distinction with the letters G, E, F 9 H, 
K. In the accompanying table are set down the values 
of B at different stages of the magnetization. 








Mean Diameter. 


10.035 cm. 

22.1 cm. 

10.735 cm. 

22.725 cm. 

Bar thickness. 






Magnetizing Force. 






















































I have the means here of illustrating the induction 
method of measuring permeability. Here is an iron 
ring, having a cross -section of almost exactly one square 
centimetre. It is wound with an exciting coil supplied 
with current by two accumulator cells ; over it is also 
wound an exploring coil of 100 turns connected in cir- 
cuit (as in Rowland's arrangement) with a ballistic gal- 
vanometer which reflects a spot of light upon yonder 
screen. In the circuit of the galvanometer is also in- 
cluded a reversing earth coil, As, a matter of fact this 



earth coil is of such a size, and wound with so many 
convolutions of wire, that when it is turned over the 
amount of cutting of magnetic lines is equal to 840,000, 
or is the same as if 840,000 magnetic lines had been cut 
once. By adjusting the resistance of the galvanometer 
circuit, it is arranged that the first swing due to the 
induced current when I suddenly turn over the earth 






coil is 8.4 scale divisions. Then, seeing that our explor- 
ing coil has 100 turns, it follows that when in our sub- 
sequent experiment with the ring we get an induced 
current from it, each division of the scale over which 
the spot swings will mean 1,000 lines in the iron. I 
turn on my exciting current. See: it swings about 11 
divisions. On breaking the circuit it swings nearly 11 
divisions, the other way. That means, that the magnetic 


ing force carries the magnetization of the iron up to 
11,000 lines; or, as the cross-section is about one square 
centimetre, B 11,000. Now, how much is H ? The 
exciting coil has 180 windings, and the exciting current 
through the amperemeter is just one ampere. The 
total excitation is just 180 "ampere turns/' We must, 
according to our rule given above, multiply this by 
1.2560 and divide by the mean circumferential length of 
the coil, which is about 32 centimetres. This makes H 
= 7. So if B = 11,000 and H = 7, the permeability 
(which is the ratio of them) is about 1,570. It is a rough 
and hasty experiment, but it illustrates the method. 

Bosanquet's experiments settled the debated question 
whether the outer layers of an iron core shield the inner 
layers from the influence of magnetizing forces. Were 
this the case, the rings made from thin bar iron should 
exhibit higher values of B than do the thicker rings. 
This is not so; for the thickest ring, G, shows through- 
out the highest magnetizations. 

(B) Bar Method. This method consists in employing 
a long bar of iron instead of a ring. It is covered from 
end to end with the exciting coil, but the exploring coil 
consists of but a few turns of wire situated just over the 
middle part of the bar. Kowland, Bosanquet, and Ewing 
have all employed this variety of method; and Ewing 
specially used bars, the length of which was more than 
100 times their diameter, in order to get rid of errors 
arising from end effects. 

(C) Divided Bar Method. This method, due to Dr. 
Hopkinson, 46 is illustrated by Fig. 17. 

* 6 JA#, Trans., 1885, p. 564, 



The apparatus consists of a block of annealed wrought 
iron about 18 inches long, 6-i wide, and 2 deep, out of 
the middle of which is cut a rectangular space to re- 
ceive the magnetizing coils. 

The test samples of iron consist of two rods, each 
12.65 millimetres in diameter, turned carefully true, 
which slide in through holes bored in the ends of the iron 
blocks. These two rods meet in the middle, their ends 


being faced true so as to make a good contact. One of 
them is secured firmly, and the other has a handle fixed 
to it, by means of which it can be withdrawn. The two 
large magnetizing coils do not meet, a space being left 
between them. Into this space is introduced the little 
exploring coil, wound upon an ivory bobbin, through 
the eye of which passes the end of the movable rod. 
The exploring coil is connected to the ballistic galva- 
nometer, B G, and is attached to an india-rubber spring 
(not shown, in the figure), which, when the rod is sucl- 


denly pulled back, causes it to leap entirely out of the 
magnetic field. The exploring coil had 350 turns of 
fine wire; the two magnetizing coils had 2,008 effective 
turns. The magnetizing current, generated by a bat- 
tery, B, of eight Grove cells, was regulated by a variable 
liquid resistance, R, and by a shunt resistance. A re- 
versing switch and an amperemeter, A, were included 
in the magnetizing circuit. By means of this apparatus 
the sample rods to be experimented upon could be sub- 
mitted to any magnetizing forces, small or large, and 
the actual magnetic condition could be examined at any 
time by breaking the circuit and simultaneously with- 
drawing the movable rod. This apparatus, therefore, 
permitted the observation separately of a series of in- 
creasing (or decreasing) magnetizations without any in- 
termediate reversals of the entire current. Thirty-five 
samples of various irons of known chemical composition 
were examined by Hopkinson, the two most important 
for present purposes being an annealed wrought iron 
and a gray cast iron, such as are used by Messrs. Mather 
and Platt in the construction of dynamo machines. 
Hopkinson embodied his results in curves, from which 
it is possible to construct, for purposes of reference, 
numerical tables of sufficient accuracy to serve for future 
calculations. The curves of these two samples of iron 
are reproduced in Fig. 18, but with one simple modifica- 
tion. British engineers, who unfortunately are con- 
demned by local circumstances to use inch measures 
instead of the international metric system, prefer to 
have the magnetic facts also stated in terms of square 
inch units instead of square centimetre units. This 



change has been made in Fig. 18, and the symbols B a 
and H /y are chosen to indicate the numbers of magnetic 
lines to the square inch in iron and in air respectively. 
The permeability or multiplying power of the iron is 

200 400 600 800 1000 1200 1400 1600 


the same, of course, in either measure. In Table II. 
are given the corresponding data in square inch meas- 
ure, and in Table III. the data in square centimetre 
measure for the same specimens of iron. 

TABLE II. (Square Inch Units.) 

Annealed Wrought Iron. 

Gray Cast Iron. 

B a 



















TABLE III. (Square Centimetre Units.) 

Annealed Wrought Iron. 

Gray Cast Iron. 


I 1 



































































It will be noted that Hopkinson's curves are double, 
there being one curve for the ascending magnetizations 
and a separate one, a little above the former, for de- 
scending magnetizations. This is a point of a little im- 
portance in designing electromagnets. Iron, and par- 
ticularly hard sorts of iron, and steel, after having been 
subjected to a high degree of magnetizing force and 
subsequently to a lesser magnetizing force, are found to 
retain a higher degree of magnetization than if the lower 
magnetizing force had been simply applied. For exam- 
ple, reference to Fig. 18 shows that the wrought iron, 
where subjected to a magnetizing force gradually rising 
from zero to H /y = 200, exhibits a magnetization of B,, 
= 95,000; but after H /y has been carried up to over 
1,000 and then reduced again to 200, B /; does not come 
down again to 95,000, but only to 98,000. Any sample 
of iron which showed great retentive qualities, or in 


which the descending curve differs widely from the as- 
cending curve, would be unsuitable for constructing 
electromagnets, for it is important that there should be 
as little residual magnetism as possible in the cores. It 
will be noted that the curves for cast iron show more of 
this residual effect than do those for wrought iron. 
The numerical data in Tables II. and III. are means 
between the ascending and descending values. 

As an example of the use of the Tables we may take 
the following: How strong must the magnetizing force 
be in order to produce in wrought iron a magnetization 
of 110,000 lines to the square inch ? Keference to Table 
II. or to Fig. 18 shows that a magnetizing field of 664 
will be required, and that at this stage of the magneti- 
zation the permeability of the iron is only 166. As there 
are 6.45 square centimetres to the square inch, 110,000 
lines to the square inch corresponds very nearly to 17,- 
000 lines to the square centimetre, and H /y = 664 cor- 
responds very nearly to H = 100. 


Another group of the methods of measuring permea- 
bility is based upon the law of magnetic traction. Of 
these there are several varieties. 

(D) Divided Ring Method. Mr. Shelford Bidwell has 
kindly lent me the apparatus with which he carried out 
this method. It consists of a ring of very soft charcoal 
iron rod 6.4 millimetres in thickness, the external diam- 
eter being eight centimetres, sawn into two half rings, 
and then each half carefully wound over with an ex- 
citing coil of insulated copper wire of 1,939 convolutions 


in' total. The two halves fit neatly together; and in 
this position it constitutes practically a continuous ring. 
When an exciting current is passed round the coils both 
halves become magnetized and attract one another. The 
force required to pull them asunder is then measured. 
According to the law of traction, which will occupy us 
in the second lecture, the tractive force (over a given 
area of contact) is proportional to the square of the 
number of magnetic lines that pass from one surface to 
the other through the contact joint. Hence the force 
of traction may be used to determine B; and on calcu- 
lating H as before we can determine the permeability. 
The following Table IV. gives a summary of Mr. Bid- 
well's results : 

TABLE IV. (Square Centimetre Measure.) Soft Charcoal Iron. 

























(E) Divided Rod Method. In this method, also used 
by Mr. Bid well, an iron rod hooked at both ends was 
divided across the middle, and placed within a vertical 
surrounding magnetizing coil. One hook was hung up 
to an overhead support; to the lower hook was hung a 
scale pan. Currents of gradually increasing strength 
were sent around the magnetizing coil from a battery 
of cells, and note was taken of the greatest weight which 


could in each case be placed in the scale pan without 
tearing asunder the ends of the rods. 

(I 7 ) Permeameter Method. This is a method which I 
have myself devised for the purpose of testing speci- 
mens of iron. It is essentially a workshop method, ns 
distinguished from a laboratory method. It requires no 
ballistic galvanometer, and the iron does not need to be 
forged into a ring or wound with a coil. For carrying it 
out a simple instrument is needed, 
which I venture to denominate as 
a permeameter. Outwardly, it has 
a general resemblance to Dr. Hop- 
kinson's apparatus, and consists, as 
you see (Fig. 19), of a rectangular 
piece of soft wrought iron, slotted 
out to receive a magnetizing coil, 
down the axis of which passes a 
brass tube. The block is 12 inches 
long, 6^ inches wide, and 3 inches 
in thickness. At one end the block 
is bored to receive the sample of 
iron that is to be tested. This consists simply of a 
thin rod about a foot long, one end of which must be 
carefully surfaced up. When it is placed inside the 
magnetizing coil and the exciting current is turned on, 
the rod sticks tightly at its lower end to the surface 
of the iron block; and the force required to detach it 
(or, rather, the square root of that force) is a measure of 
the permeation of the magnetic lines through its end 
face. In the first permeameter which I constructed the 
magnetizing coil is 13.64 centimetres in length and has 



371 turns of wire. One ampere of exciting current 
consequently produces a magnetizing force of H 34. 
The wire is thick enough to carry 30 amperes, so that 
it is easy to reach a magnetizing force of 1,000. The 
current I now turn on is 25 amperes. The two rods 
here are of "charcoal iron " and "best iron" respect- 
ively; they are of quarter-inch square stuff. Here is a 
spring balance graduated carefully, and provided with 
an automatic catch so that its index stops at the highest 
reading. The tractive force of the charcoal iron is 
about 12-J pounds, while that of the " best" iron is only 
7J pounds. B is about 19,000 in the charcoal iron, and 
H being 850, /JL is about 22.3. The law of traction which 
I use in calculating B will occupy us much in the next 
lecture; but meantime I content myself in stating it 
here for use with the permeameter. The formula for 
calculating B when the core is thus detached by a pull 
of P pounds, the area of contact being A square inches, 
is as follows: 

B = 1,317 X V P -j- A + H. 

I may add that the instrument, in its final form, was 
manufactured from my designs by Messrs. Nalder Bros., 
the well-known makers of so many electrical instru- 


In reviewing the results obtained, it will be noted that 
the curves of magnetization all possess the same general 
features, all tending toward a practical maximum, which, 
however, is different for different materials. Joule ex- 


pressed the opinion that "no force of current could gire 
an attraction equal to 200 pounds per square inch/' the 
greatest he actually attained being only 175 pounds per 
square inch. Rowland was of opinion that the limit 
was about 177 pounds per square inch for an ordinary 
good quality of iron, even with infinitely great exciting 
power. This would correspond roughly to a limiting 
value of B of about 17,500 lines to the square centime- 
tre. This value has, however, been often surpassed. 
Bidwell obtained 19,820, or possibly a trifle more, as in 
BidwelFs calculation the value of H has been needlessly 
discounted. Hopkinson gives 18,250 for wrought iron 
and 19,840 for mild Whitworth steel. Kapp gives 16,- 
740 for wrought iron, 20,460 for charcoal iron in sheet, 
and 23,250 for charcoal iron in wire. Bosanquet found 
the highest value in the middle bit of a long bar to run 
up in one specimen to 21,428, in another to 29,388, in a 
third to 27,688. Ewing, working with extraordinary 
magnetic power, forced up the value of B in Lowmoor 
iron to 31,560 (when jj. came down to 3), and subse- 
quently to 45,350. This last figure corresponds to a 
traction exceeding 1,000 pounds to the square inch. 

Cast iron falls far below these figures. Hopkinson, 
using a magnetizing force of 240, found the values of B 
to be 10,783 in gray cast iron, 12,408 in malleable cast 
iron, and 10,546 in mottled cast iron. Ewing, with a 
magnetizing force nearly 50 times as great, forced up 
the value of B in cast iron to 31,760. Mitis metal, which 
is a sort of cast wrought iron, being a wrought iron ren- 
dered fluid by addition of a small percentage of alumin- 
ium, is, as I have found, more magnetizable than cast 


iron, and not far inferior to wrought iron. It should 
form an excellent material for the cores of electromag- 
nets for many purposes where a cheap manufacture is 

A very useful alternative mode of studying the results 
obtained by experiment is to construct curves, such as 
those of Fig. 20, in which the values of the permeability 


















4.000 8.000 12.000 16.000 B / 


are plotted out vertically in correspondence with the 
values of B plotted horizontally. It will be noticed that 
in the case of Hopkinson's specimen of annealed wrought 
iron, between the points where B = 7,000 and B 
16,000 the mean values of ;*. lie almost on a straight 
line, and might be approximately calculated from the 
equation : 

n. = (17,000 B) -*- 3.5. 


Many attempts have been made, by Milller, Lamont, 
Frolich, and others to discover a simple algebraic for- 
mula whereby to express the relation between the mag- 


netizing force and the magnetism produced in the elec- 
tromagnet. According to Midler, these are related to 
one another in the same proportions as the natural 
tangent is related to the arc which it subtends. The 
formulae of Lament and Frolich, which are more nearly 
in keeping with the facts, are based upon the assump- 
tion of a relation between the permeability and the de- 
gree of magnetization present. Suppose we assume the 
approximation stated above, that the permeability is 
proportional to the difference between B and some 
higher limiting value (1 7,000 for wrought iron, 7,000 for 
cast iron). If this higher value is called /? we may write 


wnere a is a constant that varies with the quality of the 
iron or steel. 

giving by substitution and an easy transformation 
B = ^, 

which is one form of Frdlich's well-known formula. The 
constant, a, stands for the "diacritical" value of the 
magnetizing force, or that value which will bring up B 
to half the assumed limiting or " satural " value.. 

All such formula?, however convenient, are insuffi- 
cient, inasmuch as they fail to take into account the 
properties of the entire magnetic circuit. 



I have already drawn attention to the difference be- 
tween the ascending and descending curves of magneti- 
zation, and may now point out that this is a part of a 
set of general phenomena of residual effects. The best 
known of these effects is, of course, the existence in 
some kinds of iron, and notably in steel, of a remanent 
or sub-permanent magnetization after the magnetizing 


force has been entirely removed. To this retardation 
of effects behind the causes that produce them the name 
of "hysteresis" has been given by Prof. Ewing. If 
a piece of iron is subjected to a magnetizing force which 
increases to a maximum, then is decreased down to zero, 
then reversed and carried to a negative maximum, then 
decreased again to zero, and so carried round an entire 
cycle of magnetic operations, it is observed that the 
curves of magnetization form a closed area similar in 
general to those shown in Fig. 21. This closed area 


represents the work which has been wasted or dissipated 
in subjecting the iron to these alternate magnetizing 
forces. In very soft iron, where the ascending and de- 
scending curves are close together, the inclosed area is 
small, and as a matter of fact very little energy is dis- 
sipated in a cycle of magnetic operations. On the other 
hand, with hard iron, and particularly with steel, there 
is a great width between the curves and there is a great 
waste of energy. Hysteresis may be regarded as a sort 
of internal or molecular magnetic friction, by reason of 
which alternate magnetizations cause the iron to grow 
hot. Hence the importance of understanding this curi- 
ous effect, in view of the construction of electromagnets 
that are to be used with rapidly alternating currents. 
The following figures of Table V. give the number of 
watts (one watt = -^ of a horse power) wasted by hys- 
teresis in well-laminated soft wrought iron when sub- 
jected to a succession of rapid cycles of magnetization. 


Watts wasted per 

Watts wasted per 



cubic foot at 10 

cubic foot at 100 

cycles per second. 

cycles per second. 

















8,000 5i!eoo 



























It will be noted that the waste of energy increases as 


the magnetization is pushed higher and higher in a 
disproportionate degree, the waste when B is 18,000 
being six times that when B is 6,000. In the case 
of hard iron or of steel the heat waste would be far 

Another kind of after-effect was discovered by Ewing, 
and named by him " viscous hysteresis." This is the 
name given to the gradual creeping up of the magneti- 
zation when a magnetic force is applied with absolute 
steadiness to a piece of iron. This gradual creeping up 
may go on for half an hour or more, and amount to 
several per cent, of the total magnetization. 

Another important matter is that all such actions as 
hammering, rolling, twisting, and tlje like, impair the 
magnetic quality of annealed soft iron. Annealed 
wrought iron which has never been touched by a tool 
shows hardly any trace of residual magnetization, even 
after the application of magnetic forces. But the touch 
of the file will at once spoil it. Sturgeon pointed out 
the great importance of this point. In the specification 
for tenders for instruments for the British Postal Tele- 
graphs, it is laid down as a condition to be observed by 
the constructor that the cores must not be filed after 
being annealed. The continual hammering of the arma- 
ture of an electromagnet against the poles may in time 
produce a similar effect. 


I will conclude this lecture by stating a few of the 
fallacies that are current about electromagnets, and will 


add to them a few facts, some of which seem paradoxi- 
cal. The refutation of the fallacies and the explanation 
of the facts will come in due course. 

Fallacies. The attraction of an electromagnet for its 
armature varies inversely as the square of its distance 
from the poles. 

The outer windings of an electromagnet are neces- 
sarily less effective than those that are close to the iron. 

Hollow iron cores are as good as solid cores of the 
same size. 

Pole pieces add to the lifting power of an electro- 

It hurts an electromagnet (or, for that matter, a steel 
magnet) to pull oif the keeper suddenly. [It is the sud- 
den slamming on that in reality hurts it.] 

The resistance of the coil of an electromagnet ought 
to be equal to the resistance of the battery. 

A coil wound left-handedly magnetizes a magnet dif- 
ferently from a coil wound right-handedly. [It is not a 
question of winding of coil, but of circulation of current.] 

Thick wire electromagnets are less powerful than 
thin wire electromagnets. 

A badly insulated electromagnet is more powerful 
than one that is well insulated. 

A square iron core is less powerful (as Dal Negro says, 
eighteen-fold!) than a round core of equal weight. 

The attraction of an electromagnet for its keeper is 
necessarily less strong (one-third according to Du Mon- 
cel) sidewise than when the keeper is in front of the 

Putting a tube of iron outside the coils of an electro- 


magnet makes it attract a distant armature more pow- 

Facts. A bar electromagnet with a convex pole holds 
on tighter to a flat-ended armature than one with a flat 
pole does. 

A thin round disc of iron laid upon the flat round 
end of an electromagnet (the pole end being slightly 
larger than the disc), the disc is not attracted, and will 
not stick on, even if laid down quite centrally. 

If a flat armature of iron be presented to the poles 
of a horseshoe electromagnet the attraction at a short 
distance is greater, if the armature is presented flank- 
wise, than if it is presented edgewise. On the contrary, 
the tractive force in contact is greater edgewise than 

Electromagnets with long limbs are practically no 
better than those with short limbs for sticking on to 
masses of iron. 




TO-NIGHT we have to discuss the law of the magnetic 
circuit in its application to the electromagnet, and in 
particular to dwell upon some experimental results 
which have been obtained from time to time by differ- 
ent authorities as to the relation between the construc- 
tion of the various parts of an electromagnet and the 
effect of that construction on its performance. We have 
to deal not only with the size, section, length, and ma- 
terial of the iron cores, and of the armatures of iron, 
but we have to consider also the winding of the copper 
coil and its form; and we have to speak in particular 
about the way in which the shaping of the core and of 
the armature affects the performance of the electromag- 
net in acting on its armature, whether in contact or at 
a distance. But before we enter on the last more diffi- 
cult part of the subject, we will deal solely and exclu- 
sively with the law of force of the magnet upon its 
armature when the two are in contact with one another; 
in other words, with the law of traction. 

I alluded in a historical manner in my first lecture 
to the principle of the magnetic circuit, telling you how 
the idea had gradually grown up, perforce, from a con- 


sideration of the facts. The law of the magnetic cir- 
cuit was, however, first thrown into shape in 1873 by 
Professor Rowland, of Baltimore. He pointed out that 
if you consider any simple case, and find, as electricians 
do for the electric circuit, an expression for the mag- 
netizing force which tends to drive the magnetism round 
the circuit, and divide that by the resistance to magneti- 
zation reckoned also all round the circuit, the quotient 
of those two gives you the total amount of flow or flux 
of magnetism. That is to say, one may calculate the 
quantity of magnetism that passes in that way round 
the magnetic circuit in exactly the same way as one 
calculates the strength of the electric current by the law 
of Ohm. Rowland, indeed, went a great deal further 
than this, for he applied this very calculation to the ex- 
periments made by Joule more than 30 years before, and 
from those experiments deduced the degree of magnet- 
ization to which Joule had driven the iron of his mag- 
nets, and by inference obtained the amount of current 
that he had been causing to circulate. Now, this law 
requires to be written out in a form that can be used 
for future calculation. To put it in words without any 
symbols, we must first reckon out from the number of 
turns of wire in the coil, and the number of amperes 
of current which circulates in them, the whole magneto- 
motive force the whole of that which tends to drive 
magnetism along the piece of iron for it is, in fact, 
proportional to the strength of the current and the 
number of times it circulates. Next we must ascertain 
the resistance which the magnetic circuit offers to the 
passage of the magnetic lines. I here avowedly use 


Joule's own expression, which was afterward adopted 
by Rowland, and, for short, so as to avoid having four 
words, we may simply call it the magnetic resistance. 
Mr. Heaviside has suggested as an advisable alternative 
term magnetic reluctance., in order that we may not con- 
fuse the resistance to magnetism in the magnetic cir- 
cuit with the resistance to the flow of current in an 
electric circuit. However, we need not quarrel about 
terms ; magnetic reluctance is sufficiently expressive. 
Then having found these two, the quotient of them 
gives us a number representing I must not call it the 
strength of the magnetic current I will call it simply 
the quantity or number of magnetic lines which flow 
round the circuit ; or if we could adopt a term which 
is used on the continent, we might call it simply the 
magnetic flux, the flux of magnetism being the analogue 
of the flow of electricity in the electric law. The law 
of the magnetic circuit may then be stated as follows : 

magneto-motive force 
- Magnetic-flux = 

. reluctance. 

> However, it is more convenient, to -deax. with , these 
t matters in symbols, and therefore, the symbols which,! 
use, and have, long been using, ought to be explained to 
jou. For the number of spirals in a winding I use the 
letter .$/, for . the strength of current, or number of 
amperes, the letter {.; for the length of bar, or core, I 
am going to use the letter I ; for the area of cross- 
section, the letter A ; for the permeability of the iron 
which we discussed in the last lecture, the Greek sym- 
bol n; and for the total magnetic .flux, the number of 


magnetic lines, I use the letter N. Then our law be- 
comes MS follows: 

Magneto-motive f orce JQ ; 
Magnetic reluctance ~" ; 

Magnetic flux N = l ^ 


If we take the number of spirals and multiply by the 
number of amperes of current, so as to get the whole 
amount of circulation of electric current expressed in so 
many ampere turns, and multiply by 4-, and divide by 
10, in order to get the proper unit (that is to say, mul- 
tiply it by 1.257), that gives us the magneto-motive 
force. For magnetic reluctance, calculate out the reluc- 
tance exactly as you would the resistance of an electric 
conductor to the flow of electricity, or the resistance of 
a conductor of heat to the flow of heat; it will be pro- 
portional to the length, inversely proportional to the 
cross-section, and inversely proportional to the conduc- 
tivity, or, in the present case, to the magnetic permea- 
bility. Now if the circuit is a simple one, we may sim- 
ply write down here the length, and divide it by the 
area of the cross-section and the permeability, and so 
find the value of the reluctance. But if the circuit be 
not a simple one, if you have not a simple ring of iron 
of equal section all round, it is necessary to consider 


the circuit in pieces as you would an electric circuit, 
ascertaining separately the reluctance of the separate 
parts, and adding all together. As there may be a num- 
ber of such terms to be added together, I have prefixed 
the expression for the magnetic reluctance by the sign 
of summation. But it does not by any means follow, 
because we can write a thing down as simply as that, 
that the calculation of it will be a very simple mat- 
ter. In the case of magnetic lines we are quite unable 
to do as one does with electric currents, to insulate the 
flow. An electric current can be confined (provided we 
do not put it in at 10,000 volts pressure, or anything 
much bigger than that) to a copper conductor by an 
adequate layer of adequately strong and I use the 
word "strong" both in a mechanical and electrical sense 
of adequately strong insulating material. There are 
materials whose conductivity for electricity as compared 
with copper may be regarded perhaps as millions of 
millions of millions of times less; that is to say, they 
are practically perfect insulators. There are no such 
things for magnetism. The most highly insulating sub- 
stance we know of for magnetism is certainly not 10,000 
times less permeable to magnetism than the most highly 
magnetizable substance we know of, namely, iron in its 
best condition; and when one deals with electromag- 
nets where curved portions of iron are surrounded with 
copper, or with air, or other electrically insulating ma- 
terial, one is dealing with substances whose permeability, 
instead of being infinitely small compared with that of 
iron, is quite considerable. We have to deal mainly 
with iron when it has been well magnetized. Its per- 


meability competed with air is then from 1,000 to 100 
roughly; that is to say, the permeability of air compared 
with the iron is not less than from y^oth to y-oV^th part. 
That means that it is quite possible to have a very con- 
siderable leakage of magnetic lines from iron into air 
occurring to complicate one's calculations and prevent 
an accurate estimate being made of the true magnetic 
reluctance of any part of the circuit. Suppose, how- 
ever, that we have got over all these difficulties and 
made our calculations of the magnetic reluctance; then 
dividing the magneto-motive force by the reluctance 
gives us. the whole number of magnetic lines. 

There, then, is in its elementary form the law of the 
magnetic circuit stated exactly as Ohm's law is stated 
for electric circuits. But, as a general rule, one requires 
this magnetic law for certain applications, in which the 
problem is not to calculate from those two quantities 
what the total of magnetic lines will be. In most of 
the cases a rule is wanted for the purpose of calculating 
back. You want to know how to build a magnet so as 
to give you the requisite number of magnetic lines. 
You start by assuming that you need to have so many 
magnetic lines, and you require to know what magnetic 
reluctance there will be, and how much magneto-motive 
force will be needed. Well, that is a matter precisely 
analogous to those which every electrician comes across. 
He does not always want to use Ohm's law in the way 
in which it is commonly stated, to calculate the current 
from the electromotive force and the resistance; he 
often wants to calculate what is the electromotive force 
which will send a given current through a known resist- 


ance. And so do we. Our main consideration to-night 
will be devoted to the question how many ampere turns 
of current circulation must be provided in order to drive 
the required quantity of magnetism through any given 
magnetic reluctance. Therefore, we will state our law 
a little differently. What we want to calculate out is 
the number of ampere turns required. When once we 
have got that, it is easy to say what the copper wire 
must consist of, what sort of wire, and how much of it. 
Turning then to our algebraic rule, we must transform 
it, so as to get all the other things besides the ampere 
turns to the other side of the equation. So we write 
the formula: 

We shall have then the ampere turns equal to the 
number of magnetic lines we are going to force round 
the circuit multiplied by the sum of the magnetic re- 
luctances divided by 1.257. Now this number, 1.257, is 
the constant that comes in when the length I is ex- 
pressed in centimetres, the area in square centimetres, 
and the permeability in the usual numbers. Many per- 
sons unfortunately I say so advisedly because of the 
waste of brain labor that they have been compelled to 
go through prefer to work in inches and pounds and 
feet. They have, in fact, had to learn tables instead of 
acquiring them naturally without any learning. If the 
lengths be specified in inches and areas in square inches, 


then the constant is a little different. The constant in 
that case, for inch and square inch measures, is 0.3132, 
so that the formula becomes: 

Si= N X^-^ T X 0.3132, 

Here it is convenient to leave the law of the magnetic^ 
circuit, and come back to it from time to time as we 
require. What I want to point out before I go to any 
of the applications is, that with the guidance provided 
by this law, one after another the various points that 
come under review can be arranged and explained, and 
that there does not now remain if one applies this law 
with judgment a simple fact- about electromagnets 
which is either anomalous or paradoxical. Paradoxical 
some things may seem in form, but they all reduce to 
what is perfectly rational when one has a guiding prin- 
ciple of this kind to tell you how much magnetization 
you will get under given circumstances, or to tell you 
how much magnetizing power you require in order to 
get a given quantity of magnetization. I am using the 
word " magnetization " there in the popular sense, not 
in the narrow mathematical sense in which it has some- 
times been used (i. e., for the magnetic moment per unit 
cube of the material). I am using it simply to express 
the fact that the iron or air, or whatever it may be, has 
been subjected to the process which results in there 
being magnetic lines of force induced through it. 

Now let us apply this law of magnetic circuit in the 
first place to the traction, that is to say, the lifting 
power of electromagnets. The law of traction I as- 


sumed in my last lecture, for I made it the basis of a 
method of measuring the amount of permeability. The 
law of magnetic traction was stated once for all by Max- 
well, in his great treatise, and it is as follows : 

P (dynes) =. 


Where A is the area in square centimetres this be- 

B 2 A 
P (grammes) = g _ x 9gl 

That is, the pull in grammes per square centimetre 
is equal to the square of the magnetic induction, B 
(being the number of magnetic lines to the square cen- 
timetre), divided by 8~, and divided also by 981. To 
bring grammes into pounds you divide by 453.6, so that 
the formula then becomes : 

P (pounds) = 

11,183,000 ' 
or if square inch measures are used : 


P (pounds) D // 


To save future trouble we will now calculate out from 
the law of traction the following Table, in which the 
traction in grammes per square centimetre or in pounds 
per square inch is set down opposite the corresponding 
value of B. 



lines per 
sq. cm. 

B u 

lines per 
sq. in. 

sq. cencim. 

sq. ceutnn. 

sq. centim. 

sq. men. 








12,900 159,200 





19,350 358,100 
































































































14,630,000 , 










This simple statement of the law of traction assumes 
that the distribution of the magnetic lines is uniform 
all over the area we are considering; and that unfor- 
tunately is not always the case. When the distribution 
is not uniform then the mean value of the squares be- 
comes greater than the square of the mean value, and 
consequently the pull of the magnet at its end face may, 
under certain circumstances, become greater than the 
calculation would lead you to expect greater than the 
average of B would lead you to suppose. If the distri- 
bution is not uniform over the area of contact then the 
accurate expression for the tractive force (in dynes) will be 



To Galvanometer 

20 cm . 

20 cm 

the integration being taken over the whole area of con- 

This law of traction has been verified by experiment. 
The most conclusive investigations were made about 
1886 by Mr. R. H. M. Bosanquet, of Oxford, whose ap- 
paratus is depicted in Fig. 22. He took two cores of 

iron, well faced, and sur- 
rounded them both by 
magnetizing coils, fas- 
tened the upper one 
rigidly, and suspended 
the other one on a lever 
with a counterpoise 
weight. To the lower 
end of this core he hung 
a scale-pan, and meas- 
ured the traction of one 
upon the other when a 
known current was cir- 
culating a known num- 
ber of times round the 
coil. At the same time 
he placed an exploring 
coil round the joint, 
that exploring coil being connected, in the manner with 
which we were experimenting last week, with a ballistic 
galvanometer, so that at the moment when the two 
surfaces parted company, or at the moment when the 
magnetization was released by stopping the magnet- 
izing current, the galvanometer indication enabled 
him to say exactly how many magnetic lines went 




through that exploring coil. So that, knowing the 
area, you could calculate the number per square centi- 
metre, and you could therefore compare B 2 with the 
pull per square centimetre obtained directly on the 
scale-pan. Bosanquet found that even when the sur- 
faces were not absolutely perfectly faced the correspond- 
ence was very close indeed, not varying by more than 
one or two per cent, except with small magnetizing 
forces, say forces less than five 0. G. S. units. 

When one knows how irregular the behavior of iron 
is when the magnetizing forces are so small as this, 
one is not astonished to find a lack of proportionality. 
The correspondence was, however, sufficiently exact to 
say that the experiments verified the law of traction, 
that the pull is proportional to the square of the mag- 
netic induction through the area integrated over that 

Now the law of traction being in that way established, 
one at once begins to get some light upon the subject 
of the design of electromagnets. Indeed, without going 
into any mathematics, Joule had foreseen this when he 
in some instinctive sort of way seemed to consider that 
the proper way to regard an electromagnet for the pur- 
pose of traction was to think how many square inches 
of contact surface it had. He found that he could mag- 
netize iron up until it pulled with a force of 175 pounds 
to the square inch, and he doubted whether a traction 
as great as 200 pounds per square inch could be obtained. 

In the following Table Joule's results (see Table I.) 
are recalculated, and the v a,lues of B deduced : 



-- - Jteseription of 









sq. in. 

sq. cm. 



ma e g C nets..{go.3 







13, (500 




I will now return to the data in Table VI., and will 
ask you to compare the last column with the first. 
Here are various values of B, that is to say, the amounts 
of magnetization you get into the iron. You cannot 
conveniently crowd more than 20,000 magnetic lines 
through the square centimetre of the best iron, and, as 
a reference to the curves of magnetization shows, it is 
not expedient in the practical design of electromagnets 
to attempt, except in extraordinary cases, to crowd more 
than about 16,000 magnetic lines into the square centi- 
metre. The simple reason is this : that if you are work- 
ing up the magnetic force, say from up to 50, a mag- 
netizing force of 50 applied to good wrought iron will 
give you only 10,000 lines to the square centimetre, and 
the permeability by that time has fallen to about 320, 
If you try to force the magnetization any further, you 
find that you have to pay for it too heavily. If you want 
to force another 1,000 lines through the square centi- 
metre, to go from 16,000 to 17,000, you have to add on 
an enormous magnetizing force; you have to double the 
whole force from that point to get another 1,000 lines 


added. Obviously it would be much better to take a 
larger piece of iron and not to magnetize it too highly 
to take a piece a quarter as large again, and to mag- 
netize that less forcibly. It does not therefore pay to 
go much above 16,000 lines to a square centimetre 
that is to say, expressing it in terms of the law of trac- 
tion, and the pounds per square inch, it does not pay to 
design your electromagnet so that it shall have to carry 
more than about 150 pounds to the square inch. This 
shall be our practical rule : let us at once take an exam- 
ple, If you want to design an electromagnet to carry a 
load of one ton, divide the ton, of 2,240 pounds, by 150, 
and that gives the requisite number of square inches of 
wrought iron, namely, 14.92, or say 15. Of course one 
would work with a horseshoe shaped magnet, or some- 
thing equivalent something with a return circuit and 
calculate out the requisite cross-section, so that the total 
area exposed might be sufficient to carry the given load 
at 150 pounds to the square inch. And, as a horseshoe 
magnet has two poles, the cross-section of the bar of 
which it is made must be 7-J square inches. If of round 
iron, it must be about 3-| inches in diameter; if of 
square iron, it must be 2f inches each way. 

That settles the size of the iron, but not the length. 
Now, the length of the iron, if one only considers the law 
of the magnetic circuit, ought to-be as short as it can 
possibly be made. Reflect for what purpose we are de- 
signing. The design of an electromagnet is to be con- 
sidered, as every design ought to be, with a view to the 
ultimate purpose to be served by that which you are 
designing. The present purpose is the actual sticking 


on of the magnet to a heavy weight,, not acting on an- 
other magnet at a distance, not pulling at an armature 
separated from it by a thick layer of air; we are deal- 
ing with traction in contact. The question is, How 
long a piece of iron shall we need to bend over ? The 
answer is: Take length enough, and no more than 
enough, to permit of room for winding on the necessary 
quantity of wire to carry the current which will give 
the requisite magnetizing power. But this latter we do 
not yet know; it has to be calculated out by the law of 
the magnetic circuit. That is to say, we must calculate 
the magnetic flux, and the magnetic reluctance as best 
we can; then from these calculate the ampere turns of 
current; and from this calculate the needful quantity 
of copper wire, so arriving finally at the proper length 
of the iron core. It is obvious the cross-section being 
given and the value of B being prescribed, that settles 
the whole number of magnetic lines, N, that will go 
through the section. It is self-evident that length adds 
to the magnetic reluctance, and, therefore, the longer 
the length is, the greater have to be the number of 
ampere turns of circulation of the current; while the 
less the length is, the smaller need be the number of 
ampere turns of circulation. Therefore you should de- 
sign the electromagnet as stumpy as possible, that is to 
say make it a stumpy arch, even as Joule did when he 
came across the same problem, and arrived, by a sort of 
scientific instinct, at the right solution. You should have 
no greater length of iron(than is necessary in order to get 
therwindings on. Then you see>we cannot absolutely 
calculate the. length of the iron : tintil. we have an idea 


about the winding, and we must settle, therefore, pro- 
visionally, about the windings. Take a simple ideal 
case. Suppose we had an indefinitely long, straight iron 
rod, and we wound that from end to end with a mag- 
netizing coil. How thick a coil, how many ampere turns 
of circulation per inch length will you require in order 
to magnetize up to any particular degree ? It is a mat- 
ter of very simple calculation. You can calculate ex- 
actly what the magnetic reluctance of an inch length of 
the core will be. For example, if you are going to mag- 
netize up to 1G,000 lines per square centimetre, the per- 
meability will be 320. You can take the area anything 
you like, and consider the length of one inch; you can 
therefore calculate the magnetic reluctance per inch of 
conductor, and then you can at once say how many 
ampere turns per inch would be necessary in order to 
give the desired indication of 16,000 magnetic lines to 
the square centimetre. And knowing the properties of 
copper wire, and how it heats up when there is a cur- 
rent; and knowing also how much heat you can get rid 
of per square inch of surface, it is a very simple matter 
to calculate what minimum thickness of copper the fire 
insurance companies would allow you to use. They 
would not allow you to have too thin a copper wire, be- 
cause if you provide an insufficient thickness of copper 
you still must drive your amperes through it to get a 
sufficient number of ampere turns per inch of length ; 
and if you drive those amperes through copper winding 
of an insufficient thickness the copper wire will over- 
heat and your insurance policy will be revoked. You 
therefore are compelled, by the practical consideration 


of not overheating, to provide a certain thickness of 
copper wire winding. I have made a rough calculation 
for certain cases, and I find that for such small electro- 
magnets as one may ordinarily deal with, it is not nec- 
essary in any practical case to use a copper wire wind- 
ing, the total thickness of which is greater than about 
half an inch; and, as a matter of fact, if you use as 
much thickness as half an inch, you need not then wind 
the coil all along, for if you will use copper wire wind- 
ing, no matter what the size, whether thin or thick, so 
that the total thickness of copper outside the iron is 
half an inch, you can without overheating, using good 
wrought iron, make one inch of winding do for 20 inches 
length of iron. That is to say, you do not really want 
more than -^th. of an inch of thickness of copper out- 
side the iron to magnetize up to the prescribed degree 
of saturation that indefinitely long piece of which we 
are thinking, without overheating the outside surface in 
such a way as to violate the insurance rules. Take it 
approximately, if you wind to a thickness of half an 
inch the inch length of copper will magnetize 20 inches 
length of iron up to the point where B equals 16,000. 
If then we have a bar bent into a sort of horseshoe in 
order to make it stick on to a perfectly fitting armature 
also of equal section and quality, we really do not want 
more than one inch along the inner curve for every 20 
inches of iron. An extremely stumpy magnet, such as 
I have sketched in Fig. 23, will therefore do, if one can 
only get the iron sufficiently homogeneous throughout. 
If, instead of crowding the wire near the polar parts, 
we could wind entirely all round the curved part. 


though the layer of copper winding would be half an 
inch thick inside the arch, it would be much less out- 
side. Such a magnet, provided the armature fitted with 
perfect accuracy to the polar surfaces, and provided a 
battery were arranged to send the requisite number of 
amperes of current through the coils, would pull with 
a force of one ton, the iron being but 3| inches in diam- 
eter. For my own part, in this case I should prefer not 


to use round iron, one of square or rectangular section 
being more convenient; but the round iron would take 
less copper in winding, as each turn would be of mini- 
mum length if the section were circular. 

Now, this sort of calculation requires to be greatly 
modified directly one begins to deal with any other case. 
A stumpy short magnetic circuit with great cross-sec- 
tion is clearly the right thing for the greatest traction. 
You will get the given magnetization and traction with 
the least amount of magnetizing force when you have 


the area as great as possible, and the length as small as 
possible. You will kindly note that I have given you 
as yet no proofs for the practical rales that I have been 
using; they must come later. Also I have said nothing 
about the size of the wire, whether thick or thin. That 
does not in the least matter, for the ampere turns of 
magnetizing power can be made up in any desired way. 
Suppose we want on any magnet 100 ampere turns of 
magnetizing power, and we choose to employ a thin wire 
that will only carry half an ampere, then we must wind 
200 turns of that thin wire. Or, suppose we choose to 
wind it with a thick wire that will carry 10 amperes, 
then we shall want only 10 turns of that wire. The 
same weight of copper, heated up by the corresponding 
current to an equal degree of temperature, will have 
equal magnetizing power when wound on the same core. 
But the rules about winding the copper will be consid- 
ered later. 

Now if you look in the text-books that have been 
written on magnetism for information about the so- 
called lifting power or portative force of magnets in 
other words, the traction you will find that from the 
time of Bernoulli downward, the law of portative force 
has claimed the attention of experimenters, who, one 
after another, have tried to give the law of portative 
force in terms of the weight of the magnets; usually 
dealing with permanent magnets, not electromagnets. 
Bernoulli gave l a rule something of the following kind, 
which is commonly known as Hacker's rule : 

p = a 

Helvetica, III., p. 233, 1758, 


where Wis the weight of the magnet, P the greatest 
load it will sustain, and a a constant depending on the 
unit of weight chosen, on the quality of the steel and on 
its goodness of magnetization. If the weights are in 
pounds, then a is found for the best steels to vary from 
18 to 24 in magnets of horseshoe shape. This expres- 
sion is equivalent to saying that the power which a 
magnet can exert he was dealing with steel magnets; 
there were no electromagnets in Bernoulli's time is 
equal to some constant multiplied by the three-halfth 
root of the weight of the magnet itself. The rule is 
accurate only if you are dealing with a number of mag- 
nets all of the same geometrical form, all horseshoes, 
let us say, of the same general shape, made from the 
same sort of steel, similarly magnetized. In former 
years I pondered much on Hacker's rule, wondering 
how on earth the three-halfth root of the weight could 
have anything to do with the magnetic pull; and, hav- 
ing cudgeled my brains for a considerable time, I saw 
that there was really a very simple meaning in it. 
What I arrived at 2 was this: If you are dealing with a 
given material, say hard steel, the weight is proportional 
to the volume, and the cube root of the volume is some- 
thing proportional to the length, and the square of the 
cube root forms something proportional to the square 
of the length, that is to say, to something of the nature 
of a surface. What surface ? Of course the polar sur- 
face. This conTplex rule when thus analyzed turns out 
to be merely a mathematician's expression of the fact 
that the pull for a given material magnetized in a given 

3 Philosophical Magazine, Jiily, J888, 


way is proportional to the area of the polar surface; a 
law which in its simple form Joule seems to have ar- 
rived at naturally, and which in this extraordinarily 
academic form was arrived at by comparing the weights 
of magnets with the weight which they would lift. You 
will find it stated in many books that a good magnet 
will lift 20 times its own weight. There never was a 
more fallacious rule written. It is perfectly true that 
a good steel horseshoe magnet weighing one pound ought 
to be able to pull with a pull of 20 pounds on a properly 
shaped armature. But it does not follow that a mag- 
net which weighs two pounds will be able to pull with 
a force of 40 pounds. It ought not to, because a mag- 
net that weighs two pounds has not poles twice as big if 
it is the same shape. In order to have poles twice as 
big you must remember that three-halfth root coming 
in. If you take a magnet that weighs eight times as 
much, it will have twice the linear dimensions and four 
times the surface; and with four times the surface in a 
magnet of the same form, similarly magnetized, you 
will have four times the pull. With a magnet eight 
times as heavy you will have only four times the pull. 
The pull, when other things are equal, goes by surface 
and not by weight, and therefore it is ridiculous to give 
a rule saying how many times its own weight a magnet 
will pull. It is also narrated as a very extraordinary 
thing that Sir Isaac Newton had a magnet, a loadstone, 
which he wore in a signet ring, which would lift 234 
times its own weight. I have had an electromagnet 
which would lift 2,500 times its own weight, but then 
}t was a very small one, and did not weigh more than a. 


grain and a half. When you come to small things, of 
course the surface is large proportionally to the weight; 
the smaller you go, the larger becomes that dispropor- 
tion. This all shows that the old law of traction in that 
form was practically valueless, and did not guide you 
to anything at all, whereas the law of traction as stated 
by Maxwell, and explained further by the law of the 
magnetic circuit, proves a most useful rule. 

From this digression let us return to the law of the 
magnetic circuit. I gave you in my first lecture, when 
speaking of permeability, the following rule for calcu- 
lating the magnetic induction B: Take the pull in 
pounds, and the area of cross-section in square inches; 
divide one by the other, and take the square root of the 
quotient; then multiplying by 1,317 gives B; or multi- 
plying by 8,494 gives B ;/ . We have therefore a means of 
stepping from the pull per square inch to B //7 or from 
B /x to the pull per square inch. Now the other rule of 
the magnetic circuit also enables us to get from the 
ampere turns down to B /; , for we have the following 
expression for the ampere turns: 

Si=H xS-^r- X 0.3132, 
A [t 

and N, the whole number of magnetic lines in the 
magnetic circuit, is equal to B a multiplied by A", or 

N - B.A'. 

From these we can deduce a simple direct expression, 
provided we assume the quality of iron as before, and 
also assume that there is no magnetic leakage, and that 
the area of cross-section is the same all round the cir- 


cuit, in the armature as well as in the magnet core. So 
that I" is simply the mean total path of the magnetic 
lines all round the closed magnetic circuit. We may 
then write : 

Si = ^I_X 0.3132; 


B, * X 8i 

r X 0.3132 
But by the law of traction, as stated above, 

B, = 8,494 P(lbs '> 
A (sq. in.) 

Equating together these two values of B,, and solving, 
we get for the requisite number of ampere turns of cir- 
culation of exciting currents: 

Si = 2,661 x X\/ P ( lbs -) 
** ^( 

This, put into words, amounts to the following rule 
for calculating the amount of exciting power that is re- 
quired for an electromagnet pulling at its armature, in 
the case where there is a closed magnetic circuit with 
no leakage of magnetic lines. Take the square root 
of the pounds per square inch ; multiply this by the 
mean total length (in inches) all round the iron cir- 
cuit; divide by the permeability (which must be calcu- 
lated from the pounds per square inch by help of Table 
VI. and Table II.), and finally multiply by 2,661; the 
number so obtained will be the number of ampere turns. 
One goes then at once from the pull per square inch to 


the number of ampere turns required to produce that 
pull in a magnet of given length and of the prescribed 
quality. In the case where the pull is specified in kilo- 
grammes, the area of section in square centimetres, and 
the length in centimetres, the formula becomes 

#t = 3,951 . \/ 
P- v A' 

As an example, take a magnet core of round annealed 
wrought iron, half an inch in diameter, eight inches long, 
bent to horseshoe shape. As an armature, another piece, 
four inches long, bent to meet the former. Let us agree to 
magnetize the iron up to the pitch of pulling with 112 
pounds to the square inch. Reference to Table VI. shows 
that B,, will be about 90,000, and Table II. shows that in 
that case p will be about 907. From these data calculate 
what load the magnet will carry, and how many ampere 
turns of circulation of current will be needed. 

Ans. Load (on two poles) = 43.97 Ibs. 
Ampere turns needed = 372.5 

N. B. In this calculation it is assumed that the contact 
surface between armature and magnet is perfect. It never 
is; the joint increases the reluctance of the magnetic cir- 
cuit, and there will be some leakage. It will be shown later 
how to estimate these effects, and to allow for them in the 

Here let me go to a matter which has been one of the 
paradoxes of the past. In spite of Joule, and of the 
laws of traction, showing that the pull is proportional 
to the area, you have this anomaly that if you take a 
bar magnet having flat-ended poles, and measure the 
pull which its pole can exert on a perfectly flat arma- 
ture, and then deliberately spoil the truth of the con- 


tact surface, rounding it off, so making the surface gently 
convex, the convex pole, which only touches at a portion 
of its area instead of over the whole, will be found to 
exert a bigger pull than the perfectly flat one. It has 
been shown by various experimenters, particularly by 
Nickles, that if you want to increase the pull of a mag- 
net with armatures you may reduce the polar surface. 
Old steel magnets were frequently purposely made with 
a rounded contact surface. There are plenty of exam- 
ples. Suppose you take a straight round core, or one 
leg of a horseshoe, which answers equally, and take a 
flat-ended rod of iron of the same diameter as an arma- 
ture; stick it on endwise, and measure the pull when a 
given amount of ampere turns of current is circulating 
round. Then, having measured the pull, remove it and 
file it a little, so as to reduce it at the edges, or take a 
slightly narrower piece of iron, so that it will actually 
be exerting its power over a smaller area, you will get a 
greater pull. What is the explanation of this extraor- 
dinary fact ? A fact it is, and I will show it to you. 
Here, Fig. 24, is a small electromagnet which we can 
place with its poles upward. This was very carefully 
made, the iron poles very nicely faced, and on coming 
to try them it was found they were nearly equal, bin 
one pole, A, was a little stronger than the other. We 
have, therefore, rounded the other pole, B, a little, and 
here I will take a piece of iron, 0, which has itself been 
slighty rounded at one end, though it is flat at the 
other. I now turn on the current to the electromagnet, 
and I take a spring balance so that we can measure the 
pull at either of the two poles. When I put the flat end 


of C to the flat pole A so that there is an excellent con- 
tact, I find the pull about 2^ pounds. Now try the 
round end of C on the flat pole A ; the pull is about 
three pounds. The flat end of C on the round pole B 
is also about three pounds. But if now I put together 
two surfaces that are both rounded T get almost exactly 
the same pull as at first with the two flat surfaces. I 



have made many experiments on this, and so have 
others. Take the following case: There is hung up a 
horseshoe magnet, one pole being slightly convex and 
the other absolutely flattened, and there is put at the 
bottom a square bar armature, over which is slipped a 
hook to which weights can be hung. Which end of the 
armature do you think will be detached first ? 

If you were going simply by the square inches, you 
would say this square end will stick on tighter; it has 


more gripping surface. But, as a matter jf fact, the 
other sticks tighter. Why ? We are dealing here with 
a magnetic circuit. There is a certain total magnetic 
reluctance all round it, and the whole number of mag- 
netic lines generated in the circuit depends on two 
things on the magnetizing force, and on the reluctance 
all round; and, saving a little leakage, it is the same 
number of magnetic lines which come through at B as 
go through at A. But here, owing to the fact that 
there is at B a better contact at the middle than at 
the edges of the pole, the lines are crowded into a 
smaller space, and therefore at that particular place B,, 
the number of lines per square inch runs up higher, and 
when you square the larger number, its square becomes 
still larger in proportion. In comparing the square of 
smaller B a with the square of greater B a , the square of 
the smaller B y/ over the larger area turns out to be less 
than the square of the larger B a integrated over the 
smaller area. It is the law of the square coming in. 

As an example, take the case of a magnet pole formed on 
the end of a piece of round iron 1.15 inches in diameter. 
The flat pole will have 1.05 inches area. Suppose the mag- 
netizing forces are such as to make B// = 90,300, then by 
Table VI. the whole pull will be 118.75 pounds, and the 
actual number of lines through the contact surface will be 
N = 94,815. Now suppose the pole be reduced by rounding 
off the edge till the effective contact area is reduced to 0.9 
square inch. If all these lines were crowded through that 
area, that would give a rate of 105,350 per square inch. Sup- 
pose, however, that the additional reluctance and the leak- 
age reduced the number by two per cent., there would still 
be 103,260 per square inch. Reference to Table VI. shows 



that this gives a pull of 147.7 pounds per square inch, which, 
multiplied by the reduced area 0.9, gives a total pull of 132.9 
pounds, which is larger than the original pull. 

Let me show you yet another experiment. This is 
the same electromagnet (Fig. 24) which has one flat 
pole and one rounded pole. Here is an armature, also 
bent, having one flat and one rounded pole. If I put 
flat to flat and round to round, and pull at the middle, 


the flat to flat detaches first; but if we take round to 
flat and flat to round, we shall probably find they are 
about equally good it is hard to say which holds the 

The law of traction can again be applied to test the 
so-called distribution of free magnetism on the surface. 
This is a subject on which I shall have to say a good 
deal. We must therefore carefully consider what is 
meant by the phrase. Let Fig, 26 be a rough drawing 
of an ordinary bar magnet. Every one knows that if 
we dip such a magnet into iron filings the small bits of 


iron stick on more especially at the ends, but not ex- 
clusively, and if you hold it under a piece of paper or 
cardboard, and sprinkle iron filings on the paper, you 
obtain curves like those shown on the diagram. They 
attest the distribution of the magnetic forces in the 
external space. The magnetism running internally 
through the body of the iron begins to leak out sidewise, 
and, finally, all the rest leaks out in a tuft at the 
end. These magnetic lines pass round to the other end 
and there go in again. The place where the steel is 
internally most highly magnetized is this place across 
the middle, where externally no iron filings at all stick 
to it. Now, we have to think of magnetism from the 
inside and not the outside. This magnetism extends in 
lines, coming up to the surface somewhere near the 
ends of the bar, and the filings stick on wherever the 
magnetism comes up to the surface. They do not stick 
on at the middle part of the bar, where the metal is 
really most completely permeated through and through 
by the magnetism; there are a larger number of lines 
per square centimetre of cross-section in the middle 
region where none come up to the surface, and no filings 
stick on. Now, we may explore the leakage of magnetic 
lines at various points of the surface of the magnet by 
the method of traction. We can thereby arrive at a 
kind of measure of the amount of magnetism that is 
leaking, or, if you like to call it so, of the intensity of 
the "free magnetism " at the surface. I do not like to 
have to use these ancient terms, because they suggest 
the ancient notion that magnetism was a fluid or, 
rather, two fluids, one of which was plastered on at one 


end of the magnet, and the other at the other, just as 
you might put red paint or blue paint over the ends. I 
only use that term because it is already more or less 
familiar. Here is one of the ways of experimentally 
exploring the so-called distribution of free magnetism. 
The method was, I believe, originally due to Pliickcr; 
at any rate, it was much used by him. This little piece 
of apparatus was arranged by my friend and predeces- 
sor, Prof. Ayrton, for the purpose of teaching his stu- 
dents at the Finsbury College. 3 Here is a bar magnet 
of steel, marked in centimetres from end to end ; over 
the top of it there is a little steel-yard, consisting of a 
weight sliding along an arm. At the end of that steel- 
yard there is suspended a small bullet of iron. If we 
bring that bullet into contact with the bar magnet any- 
where near the end, and equilibrate the pull by sliding 
the counterpoise along the steel-yard arm, we shall ob- 
tain the definite pull required to detach that piece of 
iron. The pull will be proportional, by Maxwell's rule, 
to the square of the number of magnetic lines coming 
up from the bar into it. Shift the magnet on a whole 
centimetre, and attach the bullet a little further on; 
now equilibrate it, and we shall find it will require a 
rather smaller force to detach it. Try it again, at points 
along from the end to the middle. The greatest force 
required to detach it will be found at the extreme cor- 
ner, and a little less a little way on, and so on until we 
find at the middle the bullet does not stick on at all, 
simply because there are here no magnetic lines leaking. 
The method is not perfect, because it obviously depends 

9 See Ayrton's "Practical Electricity, 1 ' Fig. 5a, p. 24. 


on the magnetic properties of the little bullet, and 
whether it is much or little saturated with magnetism. 
Moreover, the presence of the bullet perturbs the very 
thing that is to be measured. Leakage into air is one 
thing; leakage into air perturbed by the presence of the 
little bullet of iron, which invites leakage into itself, is 
another thing. It is an imperfect experiment at the 
best, but a very instructive one. This method has 
been used again and again in various cases for exploring 
the apparent magnetism on the surface. I shall use it 
hereafter, reserving the right to interpret the result by 
the light of the law of traction. 

I now pass to the consideration of the attraction of a 
magnet on a piece of iron at a distance. And here I 
come to a very delicate and complicated question. What 
is the law of force of a magnet or electromagnet act- 
ing at a point some distance away from it ? I have a 
very great controversy to wage against the common way 
of regarding this. The usual thing that is proper to 
say is that it all depends on the law of inverse squares. 
Now, the law of inverse squares is one of those detesta- 
ble things needing to be abolished, which, although it 
may be true in abstract mathematics, is absolutely in- 
applicable with respect to electromagnets. The only 
use, in fact, of the law of inverse squares, with respect 
to electromagnetism, is to enable you to write an an- 
swer when you want to pass an academical examination, 
set by some fossil examiner, who learned it years ago at 
the University, and never tried an experiment in his 
life to see if it was applicable to an electromagnet. In 
academical examinations they always expect you to give 


the law of inverse squares. What is the law of inverse 
squares ? We had better understand what it is before 
we condemn it. It is a statement to the following eifect 
that the action of the magnet (or of the pole, some 
people say), at a point at a distance away from it, varies 
inversely as the square of the distance from the pole. 
There is a certain action at one inch away. Double the 
distance; the square of that will be four, and, inversely, 
the action will be one-quarter; at double the distance 
the action is one-quarter; at three times the distance 
the action is one-ninth, and so on. You just try it 
with any electromagnet; nay, take any magnet you 
like, and unless you hit upon the particular case, I be- 
lieve you will find it to be universally untrue. Experi- 
ment does not prove it. Coulomb, who was supposed 
to establish the law of inverse squares by means of the 
torsion balance, was working with long, thin needles of 
specially hard steel, carefully magnetized, so that the 
only leakage of magnetism from the magnet might be 
as nearly as possible leakage in radiating tufts at the 
very ends. He practically had point poles. When the 
only surface magnetism is at the end faces, the magnetic 
lines leak out like rays from a centre, in radial lines. 
Now the law of inverse squares is never true except for 
the action of points; it is a point law. If you could get 
an electromagnet or a magnet with poles so small in 
proportion to its length that you can consider the end 
face of it as the only place through which magnetic 
lines leak up into the air, and the ends themselves so 
small as to be relatively mere points; if, also, you can 
regard those end faces as something so far away from. 


whatever they are going to act upon that the distance 
between them shall be large compared with their size, 
and the end itself so small as to be a point, then, and 
then only, is the law of inverse squares true. It is a 
law of the action of points. What do we find with elec- 
tromagnets ? We are dealing with pieces of iron which 
are not infinitely long with respect to their cross-sec- 
tion, and generally possessing round or square end faces 
of definite magnitude, which are quite close to the 
armature, and which are not so infinitely far away that 
you can consider the polar face a point as compared 
with its distance away from the object upon which it is 
to act. Moreover, with real electromagnets there is 
always lateral leakage; the magnetic lines do not all 
emerge from the iron through the end face. Therefore, 
the law of inverse squares is not applicable to that case. 
What do we mean by a pole, in the first place ? We 
must settle that before we can even begin to apply any 
law of inverse squares. When leakage occurs all over a 
great region, as shown in this diagram, every portion of 
the region is polar; the word polar simply means that 
you have a place somewhere on the surface of the mag- 
net where filings will stick on; and if filings will stick 
on to a considerable way down toward the middle, all 
that region must be considered polar, though more 
strongly at some parts than at others. There are some 
cases where you can say that the polar distribution is 
such that the magnetism leaking through the surface 
acts as if there were a magnetic centre of gravity a little 
way down, not actually at the end ; but cases where you 
can say there is such a distribution as to have a mag- 


netic centre of gravity are strictly few. When Gauss 
had to make up his magnetic measurements of the 
earth, to describe the earth's magnetism, he found it 
absolutely impossible to assign any definite centre of 
gravity to the observed distribution of magnetism over 
the northern regions of the earth; that, indeed, there 
was not in this sense any definite magnetic pole to the 
earth at all. Nor is there to our magnets. There is a 


polar region, but not a pole; and if there is no centre 
of gravity of the surface magnetism that you can call a 
pole from which to measure distance, how about the law 
of inverse squares ? Allow me to show you an apparatus 
(Fig. 27), the only one I ever heard of in which the law 
of inverse squares is true. Here is a very long, thin 
magnet of steel, about three feet long, very carefully 
magnetized so as to have no leakage until quite close 
up to the end. The consequence is that for practical 
purposes you may treat this as. a magnet having point 


poles, about an inch away fr^m the ends. The south 
pole is upward and the north pole is below, resting in 
a groove in a base-board which is graduated with a scale, 
and is set in a direction east and west. I use a long 
magnet, and keep the south pole well away, so that it 
shall not perturb the action of the north pole, which, 
being small, I ask to be allowed to consider as a point. 
I am going to consider this point as acting on a small 
compass needle suspended over a card under this glass 
case, constituting a little magnetometer. If this were 
properly arranged in a room free from all other mag- 
nets, and set so that that needle shall point north, what 
will be the effect of having the north pole of the long 
magnet at some distance eastward ? It will repel the 
north end and attract the south, producing a certain de- 
flection which can be read off; reckoning the force 
which causes it by calculating the tangent of the angle 
of the deflection. Now, let us move the north pole 
(regarded as a point) nearer or farther, and study the 
effect. Suppose we halve the distance from the pole to 
the indicating needle, the deflecting force at half the 
distance is four times as great; the force at double the 
distance is one-quarter as great. Wherefore ? Because, 
firstly, we have taken a case where the distance apart 
is very great, compared with the size of the pole; sec- 
ondly, the pole is practically concentrated at a point; 
thirdly, there is only one pole acting; and fourthly, 
this magnet is of hard steel, and its magnetism in no 
way depends on the thing it is acting on, but is con- 
stant. I have carefully made such arrangements that 
the other pole shall be in the axis of rotation, so that 

\ I ... I I 


its action on the needle shall have no horizontal com- 
ponent. The apparatus is so arranged that, whatever 
the position of that north pole, the south pole, which 
merely slides perpendicularly up and down on a guide, 
is vertically over the needle, and therefore does not tend 
to turn it round in any direction whatever. With this 
apparatus one can approximately verify the law of in- 
verse squares. But this is not like 
any electromagnet ever used for any 
useful purpose. You do not make 
electromagnets long and thin, with 
point poles a very large distance 
away from the place where they 
are to act; no, you use them with 
large surfaces close up to their arm- 

There is yet another case which 
follows a law that is not a law of in- 
verse squares. Suppose you take a 

bar magnet, not too long, and ap- '&- 
proach it broadside on toward a FIG. SS.-DEFLECTION OF 
small compass needle, Fig. 28. Of j^Z^T 
course, you know as soon as you get 
anywhere near the compass needle it turns round. 
Did you ever try whether the effect is inversely pro- 
portional to the square of the distance reckoned from 
the middle of the compass needle to the middle of 
the magnet? Do you think that the deflections will 
vary inversely with the squares of the distances? 
You will find they do not. When you place the bar 
magnet like that, broadside on to the needle, the de- 


flections vary as the cube of the distance, not the 

Now, in the case of an electromagnet pulling at its 
armature at a distance, it is utterly impossible to state 
the law in that misleading way. The pull of the elec- 
tromagnet on its armature is not proportional to the 
distance, nor to the square of the distance, nor to the 
cube, nor to the fourth power, nor to the square root, 
nor to the three-half fch root, nor to any other power of 


the distance whatever, direct or inverse, because you 
find, as a matter of fact, that as the distance alters some- 
thing else alters too. If your poles were always of the 
same strength, if they did not act on one another, if 
they were not affected by the distance in between, then 
some such law might be stated. If we could always 
say, as we used to say in the old language, "at that 
pole," or "at that point," there are to be co-nsidered so 
many " units of magnetism," and at that other place so 


many units, and those are going to act on one another; 
then you could, if you wished, calculate the force by 
the law of inverse squares. But that does not corre- 
spond to anything in fact, because the poles are not 
points, and further, the quantity of magnetism on them 
is not a fixed quantity. As soon as the iron armature 
is brought near the pole of the electromagnet there is a 
mutual interaction ; more magnetic lines flow out from 
the pole than before, because it is easier for magnetic 


lines to flow through iron than through air. Let us 
consider a little more narrowly that which happens 
when a layer of air is introduced into the magnetic cir- 
cuit of an electromagnet. Here we have (Fig. 29) a 
closed magnetic circuit, a ring of iron, uncut, such as 
we experimented on last week. The only reluctance in 
the path of the magnetic lines is that of the iron, and 
this reluctance we know to be small. Compare Fig. 29 
with Fig. 30, which represents a divided ring with air- 


gaps in between the severed ends. Now, air is a less 
permeable medium for magnetic lines than iron is, or, 
in other words, it offers a greater magnetic reluctance. 
The magnetic permeability of iron varies, as we know, 
both with its quality and with the degree of magnetic 
saturation. Reference to Table III. shows that if the 
iron has been magnetized up so as to carry 16,000 mag- 
netic lines per square centimetre, the permeability at 
that stage is about 320. Iron at that stage conducts 
magnetic lines 320 times better than air does; or air 
offers 320 times as much reluctance to magnetic lines as 
iron (at that stage) does. So then the reluctance in the 
gaps to magnetization is 320 times as great as it would 
have been if the gaps had been filled up with iron. 
Therefore, if you have the same magnetizing coil with 
the same battery at work, the introduction of air-gaps 
into the magnetic circuit will, as a first effect, have the 
result of decreasing the number of magnetic lines that 
flow round the circuit. But this first effect itself pro- 
duces a second effect. There are fewer magnetic lines 
going through the iron. Consequently if there were 
16,000 lines per square centimetre before, there will now 
be fewer say only 12,000 or so. Now refer back to 
Table III. and you will find that when B is 12,000 the 
permeability of the iron is not 320, but 1,400 or so. 
That is to say, at this stage, when the magnetization of 
the iron has not been pushed so far, the magnetic re- 
luctance of air is 1,400 times greater than that of iron, 
so that there is a still greater relative throttling of the 
magnetic circuit by the reluctance so offered by the air- 



Apply that to the case of an actual electromagnet. 
Here is a diagram, Fig. 31, representing a horseshoe 
electromagnet with an armature of equal section in con- 
tact with it. The actual electromagnet for the experi- 
ment is here on the table. You can calculate out from 
the section, the length of iron and the table of permea- 



bility how many ampere turns of excitation will pro- 
duce any required pull. But now consider that same 
electromagnet, as in Fig. 32, with a small air-gap be- 
tween the armature and the polar faces. The same 
circulation of current will not now give you as much 
magnetism as before, because you have interposed air- 
gaps, and by the very fact of putting in reluctance there 
the number of magnetic lines is reduced. 


Try, if you like, to interpret this in the old way by 
the old notion of poles. The electromagnet has two 
poles, and these excite induced poles in the opposite 
surface of the armature, resulting in attraction. If 
you double the distance from the pole to the iron, the 
magnetic force (always supposing the poles are mere 
points) will be one-quarter, hence the induced pole on 
the armature will only be one-quarter as strong. But 
the pole of the electromagnet is itself weaker. How 
much weaker ? The law of inverse squares does not 
give you the slightest clue to this all-important fact. If 
you cannot say how much weaker the primary pole is, 
neither can you say how much weaker the induced pole 
will be, for the latter depends upon the former. The 
law of inverse squares in a case like this is absolutely 

Moreover, a third effect comes in. Not only do you 
cut down the magnetism by making an air-gap, but you 
have a new consideration to take into account. Be- 
cause the magnetic lines, as they pass up through one 
of the air-gaps, along the armature, down the air-gap at 
the other end, encounter a considerable reluctance, the 
whole of the magnetic lines will not go that way; a lot 
of them will take some shorter cut, although it may be 
all through air, and you will have some leakage across 
from limb to limb. I do not say you never have leakage 
under other circumst mces; even with an armature in 
apparent contact there is always a certain amount of 
sideway leakage. It depends on the goodness of the 
contact. And if you widen the air-gaps still further, 
you will have still more reluctance in the path, and still 



less magnetism, and still more leakage. Fig. 33 roughly 
indicates this further stage. The armature will be far 
less strongly pulled, because, in the first place, the in- 
creased reluctance strangles the flow of magnetic lines, 
so that there are fewer of them in the magnetic cir- 

FIG. 33. 

FIG. 34. 

cuit; and, in the second place, of this lesser number 
only a fraction reach the armature because of the in- 
creased leakage. When you take the armature entirely 
away the only magnetic lines that go through the iron 
are those that flow by leakage across the air from the 
one limb to the other. This is roughly illustrated by 
Fig. 34, the last of this set. 


Leakage across from limb to limb is always a waste of 
the magnetic lines, so far as useful purposes are con- 
cerned. Therefore it is clear that, in order to study 
the effect of introducing the distance between the arma- 
ture and the magnet, we have to take into account the 
leakage; and to calculate the leakage is no easy matter. 
There are so many considerations that occur as to that 
which one has to take into account, that it is not easy 
to choose the right ones and leave the wrong ones. 
Calculations we must make by and by they are added 
as an appendix to this lecture but for the moment ex- 
periment seems to be the best guide. 

I will therefore refer, by way of illustrating this ques- 
tion of leakage, to some experiments made by Sturgeon. 
Sturgeon had a long tubular electromagnet made of a 
piece of old musket barrel of iron wound with a coil; 
he put a compass needle about a foot away, and observed 
the effect. He found the compass needle deflected about 
23 degrees; then he got a rod of iron of equal length 
and put it in at the end, and found that putting it in 
so that only the end was introduced in the manner I 
am now illustrating to you on the table the deflection 
increased from 23 degrees to 37 degrees; but when he 
pushed the iron right home into the gun barrel it went 
back to nearly 23 degrees. How do you account for 
that ? He had unconsciously increased its facility for 
leakage when he lengthened out the iron core. And 
when he pushed the rod right home into the barrel, the 
extra leakage which was due to the added surface could 
not and did not occur. There was additional cross- 
section, but what of that ? The additional cross-section 


is practically of no account. You want to force the 
magnetism across some 20 inches of air which resists 
from 300 to 1,000 times as much as iron. What is the 
use of doubling the section of the iron ? You want to 
reduce the air reluctance, and you have not reduced the 
air by putting a core into the tube. 

There is a paradoxical experiment which we will try 
next week that illustrates an important principle. If 
you take a tubular electromagnet and put little pieces 
of iron into the ends of the iron tube that serves as 
core, and then magnetize it, the little pieces of iron will 
try to push themselves out. There is always a tendency 
to try and increase the completeness of the magnetic 
circuit; the circuit tends to rearrange itself so as to 
make it easier for the magnetic lines to go round. 

Here is another paradoxical experiment. I have here 
a bar electromagnet, which we will connect to the wires 
that bring the exciting current. In front of it, and at 
a distance from one end of the iron core, is a small com- 
pass needle with a feather attached to it as a visible in- 
dicator so that when we turn on the current the elec- 
tromagnet will act on the needle, and you will see the 
feather turn round. It is acting there at a certain dis- 
tance. The magnetizing force is mainly spent not to 
drive magnetism round a circuit of iron, but to force it 
through the air, flowing from one end of the iron core 
out into the air, passing by the compass needle, and 
streaming round again, invisible, into the other end of 
the iron core. It ought to increase the flow if we can 
in any way aid the magnetic lines to flow through the 
air. How can I aid this flow ? By putting on some- 


thing at the other end to help the magnetic lines to get 
back home. Here is a flat piece of iron. Putting it on 
here at the hinder end of the core ought to help the 
flow of magnetic lines. You see that the feather makes 
a rather larger excursion. Taking away the piece of 
iron diminishes the effect. So also in experiments on 
tractive power, it can be proved that the adding of a 
mass of iron at the far end of a straight electromagnet 
greatly increases the pulling power at the end that you 
are working with; while, on the other hand, putting the 
same piece of iron on the front end as a pole piece 
greatly diminishes the pull. Here, clamped to the table, 
is a bar electromagnet excited by the current, and here 
is a small piece of iron attached to a spring balance by 
means of which I can measure the pull required to de- 
tach it. With the current which I am employing the 
pull is about two and a half pounds. I now place upon 
the front end of the core this block of wrought iron ; it 
is itself strongly held on; but the pull which it itself 
exerts on the small piece of iron is small. Less than 
half a pound suffices to detach it. I now remove the 
iron block from the front end of the core and place it 
upon the hinder end. And now I find that the force 
required to detach the small piece of iron from the 
front end is about three and a half pounds instead of 
two and a half pounds. The front end exerts a bigger 
pull when there is a mass of iron attached to the hinder 
end. Why ? The whole iron core, including its front 
end, becomes more highly magnetized, because there is 
now a better way for the magnetic lines to emerge at 
the other end and come round to this. In short, we 


have diminished the magnetic reluctance of the air part 
of the magnetic circuit, and the flow of magnetic lines 
in the whole magnetic circuit is thereby improved. So 
it was also when the mass of iron was placed across the 
front end of the core; but the magnetic lines streamed 
away backward from its edges, and few were left in 
front to act upon the small bit of iron. So the law of 
magnetic circuit action explains this anomalous behavior. 
Facts like these have been well known for a long time 
to those who have studied electromagnets. In Stur- 
geon's book there is a remark that bar magnets pull 
better if they are armed with a mass of iron at the dis- 
tant end, though Sturgeon did not see what we now 
know to be the explanation of it. The device of fasten- 
ing a mass of iron to one end of an electromagnet in 
order to increase the magnetic power of the other end 
was patented by Siemens in 1862. 

We are now in a position to understand the bearing 
of some curious and important researches made about 
40 years ago by Dr. Julius Dub, which, like a great many 
other good things, lie buried in the back volumes of 
Poggendorff's Annalen. Some account of them is also 
given in Dr. Dub's now obsolete book, entitled "Elek- 

The first of Dub's experiments to which I will refer 
relates to the difference in behavior between electro- 
magnets with flat and those with pointed pole ends. He 
formed two cylindrical cores, each six inches long, from 
the same rod of soft iron, one inch in diameter. Either 
of these could be slipped into an appropriate magnetiz- 
ing coil. One of them had the end left flat, the other 



had its end pointed, or, rather, it was coned down until 
the flat end was left only half an inch in diameter, pos- 
sessing therefore only one-fourth of the amount of con- 
tact surface which the other core possessed. As an 
armature there was used another piece of the same soft 
iron rod, 12 inches long. The pull of the electromag- 
net on the armature at different distances was carefully 
measured, with the following results : 

Distance apart in inches. 

Pull on Flat Pole 


Pull on Pointed Pole 






















These results are plotted out in the curves in Fig. 35. 
It will be seen that in contact, and at very short dis- 
tances, the reduced pole gave the greater pull. At 
about ten mils distance there was equality, but at all 
distances greater than ten mils the flat pole had the 
advantage. At small distances the concentration of 
magnetic lines gave, in nccordance with the law of trac- 
tion, the advantage to the reduced pole. But this ad- 
vantage was, at the greater distances, more than out- 
weighed by the fact that with the greater widths of 
air-gap the use of the pole with larger face reduced the 
magnetic reluctance of the gap and promoted a larger 
flow of magnetic lines into the end of the armature. 

Dub's next experiments relate to the employment of 
polar extensions or pole-pieces attached to the core*. 



These experiments are so curious, so unexpected, unless 
you know the reasons why, that I invite your especial 
attention to them. If an engineer had to make a firm 
joint between two pieces of metal, and he feared that a 
mere attachment of one to the other was not adequately 
strong, his first and most natural impulse would be to 

20 40 60 80 100 


enlarge the parts that come together to give one, as it 
were, a broader footing against the other. And that is 
precisely what an engineer, if uninstructed in the true 
principles of magnetism, would do in order to make an 
electromagnet stick more tightly on to its armature. He 
would enlarge the ends of one or both. He would add 
pole-pieces to give the armature a better foothold. Noth- 



ing, as you will see, could be more disastrous. Dub em- 
ployed in these experiments a straight electromagnet 
having a cylindrical soft iron core, one inch in diameter, 
twelve inches long; and as armature a piece of the same 
iron, six inches long. Both were flat ended. Then six 
pieces of soft iron were prepared of various sizes, to 
serve as pole-pieces. They could be screwed on at will 
either to the end of the magnet core or to that of the 
armature. To distinguish them we will call them by 
the letters A, B, 0, etc. Their dimensions were as fel- 
lows, the inches being presumably Bavarian inches : 











Of the results obtained with these pieces we will select 
eight. They are those illustrated by the eight collected 
sketches in Fig. 36. The pull required to detach was 
measured, also the attraction exerted at a certain dis- 
tance apart. 


On Magnet. 

On Armature. 









11 5 











It will be noted that, in every case, putting on a pole- 
piece to the end of the magnet diminished both the pull 
in contact and the attraction at a distance ; it simply 
promoted leakage and dissipation of the magnetic lines. 


The worst case of all was that in which there were pole- 
pieces both on the magnet and on the armature. In 
the last three cases the pull was increased, but here the 
enlarged piece was attached to the armature, so that it 
helped those magnetic lines which came up into it to 



flow back laterally to the bottom end of the electromag- 
net, while thus reducing the magnetic reluctance of the 
return path through the air, and so, increasing the total 
number of magnetic lines, did not spread unduly those 
that issued up from the end of the core. 

The next of Dub's results relate to the effect of add- 
ing these pole-pieces to an electromagnet 12 inches 
long, which was being employed, 
broadside on, to deflect a distant 
compass needle (Fig. 37). 



None 34.5 

A 42 

B 41.5 

C 40 5 

D 41 

E 39 

F 38 

In another set of experiments 
of the same order a permanent 
magnet of steel, having polos n s, 
was slung horizontally by a bifilar 
suspension, to give it a strong 
tendency to set in a particular 
direction. At a short distance 
laterally was fixed the same bar electromagnet, and 
the same pole-pie.ces were again employed. The re- 
sults of attaching the pole-pieces at the near end are 
not very conclusive; they slightly increased the deflec- 
tion. But in the absence of information as to the d.'s- 
tance between the steel magnet and the electromagnet, 
it is difficult to assign proper values to all the causes at 
work. The results were: 




None. .. 







When, however, the pole-pieces were attached to the 
distant end of the electromagnet, where their effect 
would undoubtedly be to promote the leakage of mag- 



netic lines into the air at the front end without much 
affecting the distribution of those lines in the space in 
front of the pole, the action was more marked. 

Pole-piece Deflection 



Still confining ourselves to straight electromagnets, I 
now invite your attention to some experiments made in 
1862 by the late Count Du Moncel as to the effect of 
adding a polar expansion to the iron core. He used as 
his core a small iron tube, the end of which he could 
close up with an iron plug, and around which he placed 
an iron ring which fitted closely on to the pole. He 
used a special lever arrangement to measure the attrac- 
tion exercised upon an armature distant in all cases one 
millimetre from the pole. The results were as follows : 

Without ring 

With ring on 

on pole. 


Tubular core alone 



" with iron p 
Core provided with mass 





of iron at distant end. . 

with iron plug 



After hunting up these researches it was extremely 
interesting to find that so important a fact had not 
escaped the observant eye of the original inventor of 
the electromagnet. In Sturgeon's " Experimental Re- 
searches " (p. 113) there is a foot note, written appar- 
ently about the year 1832, which runs as follows : 

"An electromagnet of the above description, weighing 
three ounces, and furnished with one coil of wire, supported 
14 pounds. The poles were afterward made to expose a 
large surface by welding to each end of the cylindric bar a 
square piece of good soft iron ; with this alteration only the 
lifting power was reduced to about five pounds, although 
the magnet was annealed as much as possible. " 

We saw that this straight electromagnet, whether 
used broadside on or end on, could act on the compass. 


needle at some distance from it, and deflect it. In 
those experiments there was no return path for the 
magnetic lines that flowed through the iron core save 
that afforded by the surrounding air. The lines flowed 
round in wide-sweeping curves from one end to the 
other, as in Fig. 26; the magnetic field being quite ex- 
tensive. Now, what will happen if we provide a return 
path ? Suppose I surround the electromagnet with an 
iron tube of the same length as itself, the lines will flow 
along in one direction through the core, and will find 
an easy path back along the outside of the coil. Will 
the magnet thus jacketed pull more powerfully or less 
on that little suspended magnet ? I should expect it to 
pull less powerfully, for if the magnetic lines have a 
good return path here through the iron tube, why should 
they force themselves in such a quantity to a distance 
through air in order to get home ? No, they will natu- 
rally return short back from the end of the core into 
the tubular iron jacket. That is to say, the action at a 
distance ought to be diminished by putting on that iron 
tube outside. Here is the experiment set up. And you 
see that when I turn on the current my indicating 
needle is scarcely affected at all. The iron jacket causes 
that magnet to have much Jess action at a distance. 
Yet I have known people who actually proposed to use 
jacketed magnets of this sort in telegraph instruments, 
and in electric motors, on the ground that they give 
a bigger pull. You have seen that they produce less 
action at a distance across air, but there yet remains the 
question whether they give a bigger pull in contact ? 
Yes, undoubtedly they do; because everything that is 


helping the magnetism to get round to the other end 
increases the goodness of the magnetic circuit, and 
therefore increases the total magnetic flux. 

We will try this experiment upon another piece of 
apparatus, one that has been used for some years at the 
Finsbury Technical College. It consists of a straight 
electromagnet set upright in a base-board, over which is 
erected a light gallows of wood. Across the frame of 
the gallows goes a winch, on the axle of which ;s a 
small pulley with a cord knotted to it. To the lower 
end of the cord is hung a common spring balance, from 
the hook of which depends a small horizontal disc of 
iron to act as an armature. By means of the winch I 
lower this disc down to the top of the electromagnet. 
The current is turned on : the disc is attracted. On 
winding up the winch I increase the upper pull until 
the disc is detached. See, it required about nine pounds 
to pull it off. I now slip over the electromagnet, with- 
out in any way attaching it, this loose jacket of iron a 
tube, the upper end of which stands flush with the 
upper polar surface. Once more I lower the disc, and 
this time it attaches itself at its middle to the central 
pole, and at its edges to the tube. What force will now 
be required to detach it ? The tube weighs about one- 
half pound, and it is not fixed at the bottom. W^ill 
9 pounds suffice to lift the disc ? By no means. My 
balance only measures up to 24 pounds, and even that 
pull will not suffice to detach the disc. I know of one 
case where the pull of the straight core was -increased 
16-fold by the mere addition of a good return path of 
iron to complete the magnetic circuit. It is curious how 


often the use of a tubular jacket to an electromagnet 
has been reinvented. It dates back to about 1850 and 
has been variously claimed for Romershausen, for Guil- 
lemin, and for Fabre. It is described in Davis" " Mag- 
netism/' published in Boston in 1855. About sixteen 
years ago Mr. Faulkner, of Manchester, revived it under 
the name of the Altandae electromagnet. A discussion 
upon jacketed electromagnets took place in 1876 at the 
Society of Telegraph -Engineers; and in the same year 
Professor Graham Bell used the same form of electro- 
magnet in the receiver of the telephone which he exhib- 
ited at the Centennial Exhibition. But the jacketed 
form is not good for anything except increasing the 
tractive power. Jacketing an electromagnet which 
already possesses a return circuit of iron is an absurdity. 
For this reason the proposal made by one inventor to 
put iron tubes outside the coils of a horseshoe electro- 
magnet is one to be avoided. 

We will take another paradox, which equally can be 
explained by the principle of the magnetic circuit. Sup- 
pose you take an iron tube as an interior core; suppose 
you cut a little piece off the end of it; a mere ring of 
the same size. Take that little piece and lay it down 
on the end. It will be struck with a certain amount of 
pull. It will pull off easily. Take that same round 
piece of iron, put it on edgewise, where it only touches 
one point of the circumference, and it will stick on a 
good deal tighter, because it is there in a position to 
increase the magnetic flow of the magnetic lines. Con- 
centrating the flow of magnetic lines over a small sur- 
face of contact increases B at that point and B 2 , in- 


tegrated over the lesser area of the contact, gives a total 
bigger pull than is the case when the edge is touched 
all round against the edge of the tube. 

Here is a still more curious experiment. I use a cyl- 
indrical electromagnet set up on end, the core of which 
has at the top a flat, circular polar surface, about two 
inches in diameter. I now take a round disc of thin 
iron ferrotype or tin-plate will answer quite well 
which is a little smaller than the polar face. What will 
happen when this disc is laid down flat and centrally on 
the polar face ? Of course you will 
say that it will stick tightly on. If 
it does so, the magnetic lines which 
come in through its under surface 
will pass through it and come out on 
its upper surface in large quantities. 
It is clear that they cannot all, or even 
FIG. ^.-EXPERIMENT any considerable proportion of them, 
WITH TUBULAR CORE erner g e sidewise through the edges of 


the thin disc, for there is not sub- 
stance enough in the disc to carry so many magnetic 
lines. As a matter of fact the magnetic lines do come 
through the disc and emerge on its upper surface, mak- 
ing indeed a magnetic field over its upper surface that 
is nearly as intense as the magnetic field beneath its 
under surface. If the two magnetic fields were exactly 
of equal strength, the disc ought not to be attracted 
either way. Well, what is the fact ? The fact, as you 
see now that the current has been turned on, is that the 
disc absolutely refuses to lie down on the top of the 
pole. If I hold it down with my finger, it actually 


bends itself up and requires force to keep it down. I 
lift my finger, and over it flies. It will go anywhere 
in its effort to better the magnetic circuit rather than 
lie flat on top of the pole. 

Next I invite your attention to some experiments, 
originally due to Von Koike, published in the Annalen 
40 years ago, respecting the distribution of the magnetic 
lines where they emerge from 
the polar surface of an electro- 
magnet. I cannot enumerate 
them all, but will merely illus- 
trate them by a single exam- 
ple. Here is a straight electro- 
magnet with a cylindrical, flat- 
ended core (Fig. 41). In what 
way will the magnetic lines be 
distributed over it at the end ? 
Fig. 26 illustrates roughly the 
way in which, when there is no 
return path of iron, the mag- T 


lietlC lines leak through the TRIBOTION WITH SMALL IRON 

air. The main leakage is BALL * 
through the ends, though there is some at the sides 
also. Now the question of the end distribution we 
shall try by using a small bullet of iron, which will 
be placed at different points from the middle to the 
edge, a spring balance being employed to measure the 
force required to detach it. The pull at the edge is 
much stronger than at the middle, at least four or five 
times as great. There is a regular increase of pull from 
the middle to the edge. The magnetic lines, in trying 


to complete their own circuit, flow most numerously in 
that direction where they can go furthest through iron 
on their journey. They leak out more strongly at all 
edges and "corners of a polar surface. They do not flow 
out so strongly at the middle of the end surface, other- 
wise they would have to go through a larger air circuit 
to get back home. The iron is consequently more sat- 
urated round the edge than at the middle; therefore, 
with a very small magnetizing force, there is a great 
disproportion between pull at the middle and that at 
the edges. With a very large magnetizing force you do 
not get the same disproportion, because if the edge is 
already far saturated you cannot by applying higher 
magnetizing power incrsase its magnetization much, 
but you can still force more lines through the middle. 
The consequence is, if you plot out the results of a suc- 
cession of experiments of the pull at different points, 
the curves obtained are, with larger magnetizing forces, 
more nearly straight than are those obtained with small 
magnetizing forces. I have known cases where the pull 
at the edge was six or seven times as great as in the 
middle with a small magnetizing power, but with larger 
power not more than two or three times as great, al- 
though, of course, the pull all over was greater You 
can easily observe this distinction by merely putting a 
polished iron ball upon the end of the electromagnet, as 
in Fig. 42. The ball at once rolls to the edge and will 
not stay at the middle. If I take a larger two-pole 
electromagnet (like Fig. 11), what will the case now be? 
Clearly the shortest path of the magnetic lines through 
the air is the path just across from the edge of one 



polar surface to the edge of the other between the 

poles. The lines are most dense in the region where 

they arch over in as short an arch as possible, and they 

will be less dense along the 

longer paths, which arch more 

widely over. Therefore, as 

there is a greater tendency to 

leak from the inner edge of 

one pole to the inner edge of 

the other, and less tendency 

to leak from the outer edge of 

one to the outer edge of the 

other, the biggest pull ought _ 

to be On the inner edges of TO EDGE OF POLAR FACE. 

the pole. We will now try it. 

On putting the iron ball anywhere on the pole it im- 
mediately rolls until it stands perpendicularly over the 
inner edge. 

The magnetic behavior of little iron balls is very curi- 
ous. A small round piece of iron does not tend to move 
at all in the most powerful magnetic field if that mag- 
netic field is uniform. All that a small ball of iron 
tends to do is to move from a place where the magnetic 
field is weak to a place where the magnetic field is 
strong. Upon that fact depends the construction of 
several important instruments, and also certain pieces 
of electromagnetic mechanism. 

In order to study this question of leakage, and the 
relation of leakage to pul], still more incisively, I de- 
vised some time ago a small experiment with which a 
group of my students at the Technical College have 



been diligently experimenting. Here (Fig. 43) is a 
horseshoe electromagnet. The core is of soft wrought 
iron, wound with a known number of turns of wire. It 
is provided with an armature. We have also wound on 
three little exploring coils, each consisting of five turns 
of wire only, one, C, right down at the bottom on the 
bend; another, B, right round the pole, close up to the 
armature, and a third, A, around the middle of the arma- 
ture. The object of these 
is to ascertain how much 
of the magnetism which 
was created in the core by 
the magnetizing power of 
these coils ever got into the 
armature. If the armature 
is at a considerable distance 
away, there is naturally a 
great deal of leakage. The 
coil C around the bend at 
the bottom is to catch all 
the magnetic lines that go 
through the iron; the coil 
B at the poles is to catch all that have not leaked outside 
before the magnetism has crossed the joint; while the 
coil J, right around the middle of the armature, catches 
all the lines that actually pass into the armature, and 
pull at it. We measure by means of the ballistic gal- 
vanometer and these three exploring coils how much 
magnetism gets into the armature at different distances, 
and are able thus to determine the leakage, and compare 
these amounts with the calculations made, and with the 




attractions at different distances. The amount of mag- 
netism that gets into the armature does riot go by a law 
of inverse squares, I can assure you, but by quite other 
laws. It goes by laws which can only be expressed as 
particular cases of the law of the magnetic circuit. The 
most important element of the calculations, indeed, in 
many cases is the amount of percentage of leakage that 
must be allowed for. Of the magnitude of this matter 
you will get a very good idea by the result of these ex- 
periments following. 

The iron core is 13 millimetres in diameter, and the 
coil consists of 178 turns. The first swing of the gal- 
vanometer when the current was suddenly turned on or 
off measured the number of magnetic lines thereby sent 
through, or withdrawn from, the exploring coil that is 
at the time joined to the galvanometer. The currents 
used varied from 0.7 of an ampere to 5.7 amperes. Six 
sets of experiments were made, with the armature at 
different distances. The numerical results are given 
below : 





In contact 


13 870 

14 190 


1 mm 

1 552 

2 103 

3 786 

* 8 J 

2 mm 


1 487 

2 839 

si* si 

5 mm 

1 014 

1 081 

2 028 

4 *h 




1,014 . 

1 352 



In contact . . 18,240 19,590 20 283 

, 1mm 2,570 3.381 5,408 

i] 2mm 2,366 2,839 5,073 

5mm 1)352 2j2 99 5949 

1 10 mm 811 1,352 3,381 

Removed ... 1,308 3,041 


A B C 

In contact 20,940 22,280 22,960 

lmm 5,610 7,568 11,831 

38! 2mm 4 5 97 6,722 9,802 

I 5 mm 2,569 3,245 7,436 

-> 110 mm 1,149 2,704 7,098 

Removed 2,366 6,427 


A B C 

In contact 21.980 23,660 24,040 

f 1mm 8,110 10,810 17,220 

2mm 5,611 8,464 15,886 

5mm 4,056 5,273 12,627 

[10 mm 2,029 4,057 10,142 

Removed 3,581 9,795 

These numbers may be looked upon as a kind of 
numerical statement of the facts roughly depicted in 
Figs. 31 to 34. The numbers themselves, so far as they 
relate to the measurements made (1) in contact, (2) with 
gaps of one millimetre breadth, are plotted out on Fig. 
44, there being three curves, A, B and (7, for the meas- 
urements m^de when the armature was in contact,, and 



three others, A\, BI, C\, made at the one millimetre dis- 
tance. A dotted line gives the plotting of the numbers 
for the coil C, with different currents, when the arma- 
ture was removed. 

On examining the numbers in detail we observe that 
the largest number of magnetic lines forced round the 
bend of the iron core, through the coil C, was 24,040 
(the cross-section being a little over one square centi- 


'100 500 1000 


metre), which was when the armature was in contact. 
When the armature was away the same magnetizing 
power only eVoked 9,795 lines. Further, of those 24,- 
040, 23,660 (or 98^ per cent.) came up through the polar 
surfaces of contact, and of those again 21,980 (or 92| per 
cent, of the whole number) passed through the arma- 
ture. There was leakage, then, even when the armature 
was in contact, but it amounted to only 7-j- per cent. 
Now, when the armature was moved but one millimetre 


(i. e., one twenty-fifth of an inch) away, the presence of 
the air-gaps had this great effect, that the total mag- 
netic flux was at once choked down from 24,040 to 17,- 
220. Of that number only 10,810 (or 61 per cent.) 
reached the polar surfaces, and only 8,110 (or 47 per 
cent, of the total number) succeeded in going through 
the armature. The leakage in this case was 53 per 
cent. ! With a two millimetre gap the leakage was 65 
per cent, when the strongest current was used. It was 
68 per cent, with a five millimetre gap, and 80 per cent, 
with a 10 millimetre gap. It will further be noticed 
that while a current of 0.7 ampere sufficed to send 12,- 
506 lines through the armature when it was in contact, 
a current eight times as strong could only succeed in 
sending 8,110 lines when the armature was distant by a 
single millimetre. 

Such an enormous diminution in the magnetic flux 
through the armature, consequent upon the increased 
reluctance and increased leakage occasioned by the pres- 
ence of the air-gaps, proves how great is the reluctance 
offered by air, and how essential it is to have some prac- 
tical rules for calculating reluctances and estimating 
leakages to guide us in designing electromagnets to do 
any given duty. 

The calculation of magnetic reluctances of definite 
portions of a given material are now comparatively 
easy, and, thanks to the formulae of Prof. Forbes, it is 
now possible in certain cases to estimate leakages. Of 
these methods of calculation an abstract will be given 
in the appendix to this lecture. I have, however, found 
Forbes' rules, which were intended to aid the design of 


dynamo machines, not very convenient for the common 
cases of electromagnets, and have therefore cast about 
to discover some more apposite mode of calculation. To 
predetermine the probable percentage of leakage one 
must first distinguish between those magnetic lines 
which go usefully through the armature (and help to 
pull it) and those which go astray through the sur- 
rounding air and are wasted so far as any pull is con- 
cerned. Having set up this distinction, one then needs 
to know the relative magnetic conductance, or permeance, 
along the path of the useful lines, and that along the 
innumerable paths of the wasted lines of the stray field. 
For (as every electrician accustomed to the problems 
of shunt circuits will recognize) the quantity of lines 
that go respectively along the useful and wasteful paths 
will be directly proportional to the conductances (or 
permeances) along those paths, or will be inversely pro- 
portional to the respective resistances along those paths. 
It is customary in electromagnetic calculations to em- 
ploy a certain coefficient of allowance for leakage, the 
symbol for which is v, such that when we know the 
number of magnetic lines that are wanted to go through 
the armature we must allow for v times as many in the 
magnet core. Now, x if u represents permeance along the 
useful path, and w the permeance of all the waste paths 
along the stray field, the total ftux will be to the use- 
ful Rux as u -|- w is to u. Hence the coefficient of 
allowance for leakage v is equal to u -\- w divided by u. 
The only real difficulty is to calculate u and w. In gen- 
eral u is easily calculated; it is the reciprocal of the 
sum of all the mngnetic reluctances along the useful 



path from pole to pole. In the case of the electromag- 
net used in the experiments last described, the magnetic 
reluctances along the useful path are three in number, 
that of the iron of the armature and those of the two 
air-gaps. The following formula is applicable, 


reluctance = 


if the data are specified in centimetre measure, the suf- 
fixes 1 and 2 relating respectively to the iron and to the 
air. If the data are specified in inch measures the for- 
mula becomes 

reluctance = 0.3132 

/ A" ' A'- 
\ JH if*i J 

But it is not so easy to calculate the reluctance (or its 
reciprocal, the permeance) for the 
waste lines of the stray field, be- 
cause the paths of the magnetic 
lines spread out so extraordinarily 
and bend round in curves from 
pole to pole. 

Fig. 45 gives a very fair repre- 
sentation of the spreading of the 
lines of the stray field that leaks 
across between the two limbs of a 
horseshoe electromagnet made of 
round iron. And for square iron 
the flow is much the same, except 
that it is concentrated a little by 
the corners of the metal. Forbes 7 rules do not help us 
here. We want a new mode of considering the subject. 



The problems of flow, whether of heat, electricity or 
of magnetism, in space of three dimensions, are not 
among the most easy of geometrical exercises. How- 
ever, some of them have been worked out, and may be 
made applicable to our present need. Consider, for 
example, the electrical problem of finding the resistance 
which an indefinitely extended liquid (say a solution of 
sulphate of copper of given density) offers when acting 
as a conductor of electric currents flowing across between 
two indefinitely long parallel cylinders of copper. Fig. 
45 may be regarded as representing a transverse section 
of such an arrangement, the sweeping curves represent- 
ing lines of flow of current. In a simple case like this 
it is possible to find an accurate expression for the re- 
sistance (or of the conductance) of a layer or stratum of 
unit thickness. It depends on the diameters of the 
cylinders, on their distance apart, and on the specific 
conductivity of the medium. It is not by any means 
proportional to the distance between them, being, in 
fact, almost independent of the distance, if that is 
greater than 20 times the perimeter of either cylinder. 
Neither is it even approximately proportional to the 
perimeter of the cylinders except in those cases when 
the shortest distance between them is less than a tenth 
part of the perimeter of either. The resistance, for 
unit length of the cylinders, is, in fact, calculated out 
by the rather complex formula : 

R = log. nat. h; 

n = 



1i4( . r r I- 

the symbol a standing for the radius of the cylinder; b 
for the shortest distance separating them; /j. for the 
permeability, or in the electric case the specific conduc- 
tivity of the medium. 

Now, I happened to notice, as a matter that greatly 
simplifies the calculation, that if we confine our atten- 
tion to a transverse layer of the medium of given thick- 
ness, the resistance be- 
tween the two bits of the 
cylinders in that layer 
depends on the ratio of 
the shortest distance sep- 
arating them to their 
periphery, and is inde- 
pendent of the absolute 
size of the system. If 
you have the two cylin- 
ders an inch round and 
an inch between them, 
then the resistance of the 
slab of medium (of given 
thickness) in which they 
lie will be the same as if 

they were a foot round and a foot apart. Now that sim- 
plifies matters very much, and thanks to my friend and 
former chief assistant, Dr. R. Mullineux Walmsley, who 
devoted himself to this troublesome calculation, I am 
able to give you, in tabular form, the magnetic resist- 
ances within the limits of proportion that are likely to 






Magnetic reluctance in C. G. 
S. units = the magneto-mo- 

Magnetic reluctance in inch 
units the ampere turns -f- 

Ratio of least 

tive force -*- total magnetic 

the total magnetic flux. 
Slab = 1 inch thick. 

distance apart 

to perimeter. 


























































































NOTE. In the above table, unit length of cylinders is assumed (1 centimetre 
in columns 2 and 3 ; 1 inch in columns 4 and 5) ; the flow of magnetic lines 
being reckoned as in a slab of infinite extent and of unit thickness. Sym- 
bols : p = perimeter of cylinder ; b = shortest distance between cylinders. 
In columns 2 and 3 the unit reluctance is that of a centimetre cube of air. In 
columns 4 and 5 the unit reluctance is so chosen (as in the rest of these lec- 
tures wherever such measures are used) that the reduction of ampere turns 
to magneto-motive force by multiplying by4n--r-10 is avoided. This will 
make the reluctance of the inch cube of air equal to 10 -s- 4w -s- 2.54 = 0.3132, 
and its permeance as 3.1931. 

The numbers from columns 1 and 2 of the preceding 
table are plotted out graphically in Fig. 46 for more 
convenient reference. As an example of the use of the 
table we will take the following : 

EXAMPLE. Find the magnetic reluctance and permeance 
between two parallel iron cores of one inch diameter and 


nine inches long, the least distance between them being 2$- 
inches. Here b = 2.375; p = 3.1416; b H- p = 0.756. Refer- 
ence to the table shows (by interpolation) that the reluc- 
tance and permeance for unit thickness of slab are respect- 
ively 0.183 and 5.336. For nine inches thickness they will 
therefore be 0.021 and 48.02 respectively. 

"When the permeance across between the two limbs is 
thus approximately calculable, the waste flux across the 
space is estimated by multiplying the permeance so 
found by the average value of the difference of magnetic 
potential between the two limbs. And this, if the yoke 
which unites the limbs at their lower end is of good 
solid iron, and if the parallel cores offer little magnetic 
reluctance as compared with the reluctance of the use- 
ful paths, or of that of the stray field, may be simply 
taken as half the ampere turns (or, if centimetre meas- 
ures are used, multiply by 1.2566). 

The method here employed in estimating the reluc- 
tance of the waste field is of course only an approxima- 
tion; for it assumes that the leakage takes place only in 
the planes of the slabs considered. As a matter of fact 
there is always some leakage out of the planes of the 
slabs. The real reluctance is always therefore some- 
what less, and the real permeance somewhat greater, 
than that calculated from Table VIII. 

For the electromagnets used in ordinary telegraph 
instruments the ratio of b to p is not usually very dif- 
ferent from unity, so that for them the permeance across 
from limb to limb per inch length of core is not very 
far from 5.0, or nearly twice the permeance of an inch 
cube of air. 


We are now in a position to see the reason for a curi- 
ous statement of Count Du Moncel which for long puz- 
zled me. He states that he found, using distance apart 
of one millimetre, that the attraction of a two-pole elec- 
tromagnet for its armature was less when the armature 
was presented laterally than when it was placed in front 
of the pole-ends, in the ratio of 19 to 31. He does not 
specify in the passage referred to what was the shape 
of either the armature or the cores. If we assume that 
he was referring to an electromagnet with cores of the 
usual sort round iron with flat ends, presumably like 
Fig. 11 then it is evident that the air-gaps, when the 
armature is presented sidewise to the magnet, are really 
greater than when the armature is presented in the 
usual way, owing to the cylindric curvature of the core. 
So, if at equal measured distance the reluctance in the 
circuit is greater, the magnetic flux will be less and the 
pull less. 

It ought also now to be evident why an armature 
made of iron of a flat rectangular section, though when 
in contact it sticks on tighter edgewise, is at a distance 
attracted more powerfully if presented flatwise. The 
gaps, when it is presented flatwise (at an equal least dis- 
tance apart), offer a lesser magnetic reluctance. 

Another obscure point also becomes explainable, 
namely, the observation by Lenz, Barlow, and others, 
that the greatest amount of magnetism which could be 
imparted to long iron bars by a given circulation of 
electric current was (nearly) proportional, not to the 
cross-sectional area of the iron, but to its surface! The 
explanation is this: Their magnetic circuit was a bad 



one, consisting of a straight rod of iron and of a return 
path through air. Their magnetizing force was being 
in reality expended not so much on 'driving magnetic 
lines through iron (which is readily permeable), but on 
driving the magnetic lines through air (which is, as we 
know, much less permeable), and the reluctance of the 
return paths through the air is when the distance 
from one to the other of the exposed end parts of the 
bar is great compared with its per- 
iphery very nearly proportional to 
that periphery, that is to say, to the 
exposed surface. 

Another opinion on the same topic 
was that of Prof. Miiller, who laid 
down the law that for iron bars of 
equal length, and excited by the 
same magnetizing power, the amount 
of magnetism was proportional to 
the square root of the periphery. A 
vast amount of industrious scientific 
effort has been expended by Dub, 
Hankel, Von Feilitzsch, and others 
on the attempt to verify this " law." Not one of these ex- 
perimenters seems to have had the faintest suspicion that 
the real thing which determined the amount of mag- 
netic flow was not the iron, but the reluctance of the re- 
turn path through air. Von Feilitzsch plotted out the 
accompanying curves (Fig. 47), from which he drew the 
inference that the law of the square root of the periphery 
was established. The very straightness of these curves 
shows that in no case had the iron become so much 

FIG. 47. VON FEI- 


magnetized as to show the bend that indicates approach- 
ing saturation. Air, not iron, was offering the main 
part of the resistance to magnetization in the whole of 
these experiments. I draw from the very same curves 
the conclusion that the magnetization is not propor- 
tional to the square root of the periphery, but is more 
nearly proportional to the periphery itself; indeed, the 
angles at which the different curves belonging to the 
different peripheries rise show that the amount of mag- 
netism is very nearly as the surface. Observe here we 
are not dealing with a closed magnetic circuit where 
section comes into account; we are dealing with a bar 
in which the magnetism can only get from one end to 
the other by leaking all round into the air. If, there- 
fore, the reluctance of the air path from one end of the 
bar to the other is proportional to the surface, we should 
get some curves very like these ; and that is exactly 
what happens. If you have a solid, of a certain given 
geometrical form, standing out in the middle of space, 
the conductance which the space around it (or rather 
the medium filling that space) offers to the magnetic 
lines flowing through it, is practically proportional to 
the surface. It is distinctly so for similar geometrical 
solids, when they are relatively small as compared with 
the distance between them. Electricians know that the 
resistance of the liquid between two small spheres, or 
two small discs of copper immersed in a large bath of 
sulphate of copper, is practically independent of the 
distance between them, provided they are not within 
ten diameters, or so, of one another. In the case of a 
long bar we may treat the distance between the protrud- 


ing ends as sufficiently great to make an approximation 
to this law hold good. Von Feilitzsch's bars were, how- 
ever, not so long that the average value of the length of 
path from one end surface to the other end surface, 
along the magnetic lines, was infinitely great as com- 
pared with the periphery. Hence the departure from 
exact proportionality to the surface. His bars were 9.1 
centimetres long, and the peripheries of the six were 
respectively 94.9, 90.7, 79.2, 67.6, 54.9 and 42.9 millime- 

It has long been a favorite idea with telegraph en- 
gineers that a long-legged electromagnet in some way 
possessed a greater " protective " power than a short- 
legged one; that, in brief, a long-legged magnet could 
attract an armature at a greater distance from its poles 
than could a short-legged one made with iron cores of 
the same section. The reason is not far to seek. To 
project or drive the magnetic lines across a wide inter- 
vening air-gap requires a large magnetizing force on 
account of the great reluctance, and the great leakage 
in such cases. And the great magnetizing force cannot 
be got with short cores, because there is not, with short 
cores, a sufficient length of iron to receive all the turns 
of wire that are in such a case essential. The long leg 
is wanted simply to carry the wire necessary to provide 
the requisite circulation of current. 

We now see how, in designing electromagnets, the 
length of the iron core is really determined; it must be 
long enough to allow of the winding upon it of the wire 
which, without overheating, will carry the ampere turns 
of exciting current which will suffice to force the requi- 


site number of magnetic lines (allowing for leakage) 
across the reluctances in the useful path. We shall 
come back to this matter after we have settled the mode 
of calculating the quantity of wire that is required. 

Being now in a position to calculate the additional 
magnetizing power required for forcing magnetic lines 
across an air-gap, we are prepared to discuss a matter 
that has been so far neglected, namely, the effect on the 
reluctance of the magnetic circuit of joints in the iron. 
Horseshoe electromagnets are not always made of one 
piece of iron bent round. They are often made, like 
Fig. 11, of two straight cores shouldered and screwed, or 
riveted into a yoke. It is a matter purely for experi- 
ment to determine how far a transverse plane of section 
across the iron obstructs the flow of magnetic lines. 
Armatures, when in contact with the cores, are never 
in perfect contact, otherwise they would cohere without 
the application of any magnetizing force; they are only 
in imperfect contact, and the joint offers a considerable 
magnetic reluctance. 

This matter has been examined by Prof. J. J. Thom- 
son and Mr. Newall, in the Cambridge Philosophical 
Society's Proceedings, in 1887; and recently more fully 
by Prof. Ewing, whose researches are published in the 
Philosophical Magazine for September, 1888. Ewing 
not only tried the effect of cutting and of facing up 
with true plane surfaces, but used different magnetizing 
forces, and also applied various external pressures to the 
joint. For our present purpose we need not enter into 
the questions of external pressures, but will summarize 
the results which Ewing found when his bar of wrought 



iron was cut across by section planes, first into two 
pieces, then into four, then into eight. The apparent 
permeability of the bar was reduced at every cut. 


Mean thickness of 

Thiekness of iron 


equivalent air- 
space for one 

of equivalent 
reluctance per 





Cut in 




















































Suppose we are working with the magnetization of 
our iron pushed to about 16,000 lines to the square cen- 
timetre (i. e. y about 150 pounds per square inch, trac- 
tion), requiring a magnetizing force of about H = 50; 
then, referring to the table, we see that each joint 
across the iron offers as much reluctance as would an 
air-gap 0.0005 of an inch in thickness, or adds as much 
reluctance as if an additional layer of iron about one- 
sixth of an inch thick had been added. With small 
magnetizing forces the effect of having a cut across the 
iron with a good surface on it is about the same as 
though you had introduced a layer of air one six-hun- 
dredth of an inch thick, or as though you had added to 
the iron circuit about one inch of extra length. With 
large magnetizing forces, however, this disappears, prob- 
ably because of the attraction of the two surfaces across 
that cut. The stress in the magnetic circuit with high 



magnetic forces running up to 15,000 or 20,000 lines to 
the square centimetre will of itself put on a pressure of 
130 to 230 pounds to the square inch, and so these resist- 
ances are considerably reduced; they come down in fact 
to about one-twentieth of their initial value. When 
Ewing specially applied compressing forces, which were 
as large as 670 pounds to the square inch, which would 
of themselves ordinarily, in a continuous piece of iron, 
have diminished the mag- 
netizability, he found the 
diminution of the magnet- 
izability of iron itself was 
nearly compensated for by 
the better conduction of 
the cut surface. The old 
sn rf ace, cut and compressed 
in that way, closes up as 
it were, magnetically - 
does not act like a cut at 
all; but at the same time 
you lose just as much as you 
gain, because the iron itself 
becomes less magnetizable. 

The above results of Swing's are further represented 
by the curves of magnetization drawn in Fig. 48. When 
the faces of a cut were carefully surfaced up to true 
planes, the disadvantngeous effect of the cut was re- 
duced considerably, find, under the application of a heavy 
external pressure, almost vanished. 

I have several times referred to experimental results 
obtained in past years, principally by German and 



French workers, buried in obscurity in the pages of 
foreign scientific journals. Too often, indeed, the 
scattered papers of the German physicists are rendered 
worthless or unintelligible by reason of the omission of 
some of the data of the experiments. They give no 
measurements perhaps of their currents, or they used 
an uncalibrated galvanometer, or they do not say how 
many windings they were using in their coils ; or per- 
haps they give their results in some obsolete phraseol- 
ogy. They are extremely addicted to informing you 
about the " magnetic moments " of their magnets. Now 
the magnetic moment of an electromagnet is the one 
thing that one never wants to know. Indeed the mag- 
netic moment of a magnet of any kind is a useless piece 
of information, except in the case of bar magnets of 
hard steel that are to be used in the determination of 
the horizontal component of the earth's magnetic force. 
What one does want to know about an electromagnet 
is the number of magnetic lines flowing through its cir- 
cuit, and this the older researches rarely afford the 
means of ascertaining. Nevertheless, there are some 
investigations worthy of study to which time will now 
only permit me very briefly to allude. These are the 
researches of Dub on the effect of thickness of arma- 
tures, and those of Nickles and of Du Moncel on the 
lengths of armatures. Also those of Nickles on the 
effect of width between the two limbs of the horseshoe 

I can only now describe some experiments of Von 
Feilitzsch upon the vexed question of tubular cores, a 
matter touched by Sturgeon, Pfaff, Joule, Nickles, and 



later by Du Moncel. To examine the question whether 
the inner part of the iron really helps to carry the mag- 
netism, Von Feilitzsch prepared a set of thin iron tubes 
which could slide inside one another. They were all 
11 centimetres long, and their peripheries varied from 
6.12 centimetres to 9.7 centimetres. They could be 
pushed within a magnetizing spiral to which either 
small or large currents could be applied, and their effect 
in deflecting a magnetic needle was 
noted, and balanced by means of a 
compensating steel magnet, from 
the position of which the forces 
were reckoned and the magnetic 
moments calculated out. As the 
tubes were of equal lengths, the 
magnetization is approximately 
proportional to the magnetic mo- 
ment. The outermost tube was 

u 240 a jo 

first placed in the spiral, and a set 

, .. -IT ,-,,-, FIG. 49. VON FEILITZSCH'S 

of observations made; then the tube CURVES OP MAGNKTIZA- 
of next smaller size was slipped TION OF TuBES - 
into it and another set of observations made; then 
a third tube was slipped in until the whole of the 
seven were in use. Owing to the presence of the outer 
tube in all the experiments, the reluctance of the air 
return paths was alike in every case. The curves given 
in Fig. 49 indicate the results. 

The lowest curve is that corresponding to the use of 
the first tube alone. Its form, bending over and be- 
coming nearly horizontal, indicates that with large 
magnetizing power it became nearly saturated. The 



second curve corresponds to the use of the first tube 
with the second within it. With greater section of iron 
saturation sets in at a later stage. Each successive tube 
adds to the capacity for carrying magnetic lines, the 
beginning of saturation being scarcely perceptible, even 
with the highest magnetizing power, when all seven 
tubes were used. All the curves have the same initial 
slope. This indicates that with small magnetizing 
forces, and when even the least quantity of iron was 
present, when the iron was far from saturation, the 
main resistance to magnetization was that of the air 
paths, and it was the same whether the total section of 
iron in use was large or small. 

I must leave till my next lecture the rules relating to 
the determination of the windings of copper wire on 
the cores. 



Symbols used. 

N = the whole number of magnetic lines (C.G. S. defini- 
tion of magnetic lines, being one line per square 
centimetre to represent intensity of a magnetic 
field, such that there is one dyne on unit magnetic 
pole) that pass through the magnetic circuit. 
Also called the magnetic flux. 

B = the number of magnetic lines per square centi- 
metre in the iron; also called the induction* or 
the internal magnetization. 

B /7 = the number of magnetic lines per square inch 
in the iron. 

H the magnetic force or intensity of the magnetic 
field, in terms of the number of magnetic lines 
to the square centimetre that there would be in 

H^ the magnetic force, in terms of the number of 
magnetic lines that there would be to the square 
inch, in air. 

P. = the permeability of the iron, etc. ; that is its mag- 
netic conductivity or multiplying power for mag- 
netic lines. 

A = area of cross-section, in square centimetres. 


A" = area of cross-section, in square inches. 

I = length, in centimetres. 

I" = length, in inches. 

8 = number of spirals or turns in the magnetizing 


i = electric current, expressed in amperes. 
v = coefficient of allowance for leakage; being the 

ratio of the whole magnetic flux to that part of 

it which is usefully applied. (It is always greater 

than unity.) 

Relations of units. 

1 inch = 2.54 centimetres; 

1 centimetre 0.3937 inch. 

1 square inch = 6.45 square centimetres; 

1 square centimetre = 0.1550 square inch. 

1 cubic inch 16.39 cubic centimetres ; 

1 cubic centimetre = 0.0610 cubic inch. 

To calculate the value of B or of B^from the traction. 

If P denote the pull, and A the area over which it 
is exerted, the following formulae (derived from Max- 
welFs law) may be used : 

B = 4,965 A 7 J kilos ' 

A sq. cm.' 

B = 1,316.6 \/ 


A sq. in. 9 

- . 

A s. m, 



To calculate the requisite cross-section of iron for a given 

Reference to p. 89 will show that it is not expedient 
to attempt to employ tractive forces exceeding 150 
pounds per square inch in magnets whose cores are of 
soft wroughfc iron, or exceeding 28 pounds per square 
inch in cast iron. Dividing the given load that is to be 
sustained by the electromagnet by one or other of these 
numbers gives the corresponding requisite sectional 
area of wrought or cast iron respectively. 

To calculate the permeability from B or from B^. 

This can only be satisfactorily done by referring to a 
numerical Table (such as Table II. or IV.), or to graphic 
curves, such as Fig. 18, in which are set down the re- 
sult of measurements made on actual samples of iron of 
the quality that is to be used. The values of IJL for the 
two specimens of iron to which Table II. refers may 
be approximately calculated as follows : 

^ 17,000 - B 

For annealed wrought iron, // = - ; 


7,000 - B 

For gray cast iron, /JL = . 


These formulae must not be used for the wrought 
iron for tractions that are less than 28 pounds per 
square inch, nor for cast iron for tractions less than 2% 
pounds per square inch, 


To calculate the total magnetic flux which a core of 
given sectional area can conveniently carry. 

It has been shown that it is not expedient to push 
the magnetization of wrought iron heyond 100,000 
lines to the square inch, nor that of cast iron beyond 
42,000. These are the highest values that ought to be 
assumed in designing electromagnets. The total mag- 
netic flux is calculated by multiplying the figure thus 
assumed by the number of square inches of sectional 

To calculate the magnetizing power requisite to force a 
given number of magnetic lines through a definite 
magnetic reluctance. 

Multiply the number which represents the magnetic 
reluctance by the total number of magnetic lines that 
are to be forced through it. The product will be the 
amount of magneto-motive force. If the magnetic re- 
luctance has been expressed on the basis of centimetre 
measurements, the magneto-motive force, calculated as 

above, will need to be divided by 1.2566 ft. e. t by ^j 

to give the number of ampere turns of requisite magnet- 
izing power. If, however, the magnetic reluctance has 
been expressed in the units explained below, based 
upon inch measures, the magnetizing power, calculated 
by the rule given above, will already be expressed 
directly in ampere turns, 


To calculate the magnetic reluctance of an iron core. 

(a.) If dimensions are given in centimetres. Mag- 
netic reluctance being directly proportional to length, 
and inversely proportional to sectional area and to per- 
meability, the following is the formula : 

Magnetic reluctance - ; 

A p. 

but the value of /JL cannot be inserted until one knows 
how great B is going to be; when reference to Table II. 
gives fj.. 

(b.) If dimensions are given in inches. In this case 
we can apply a numerical coefficient, which takes into 
account the change of units (2.54), and also, at the 
same time, includes the operation of dividing the mag- 
neto-motive force by T 4 ^ of TT ( = 1.2566) to reduce it to 
ampere turns. 80 the rule becomes 


Magnetic reluctance = -^ X 0.3132. 

Example. Find the magnetic reluctance from end to end 
of a bar of wrought iron 10 inches long, with a cross-section 
of 4 square inches, on the supposition that the magnetic 
flux through it will amount to 440,000. 

To calculate the total magnetic reluctance of a mag- 
netic circuit. 

This is done by calculating the magnetic reluctances 
of the separate parts, and adding them together. Ac- 
count must, however, be taken of leakage; for when the 
flux divides, part going through an armature, part 



through a leakage path, the law of shunts comes in, and 
the net reluctance of the joint paths is the reciprocal of 
the sum of their reciprocals, In the simplest case the 
magnetic circuit consists of three parts, (1) armature, 
(2} air in the two gaps, (3) core of the magnet. These 
three reluctances may be separately written thus: 

For Centimetre Measure. 

For Inch Measure. 

1A vrnflturp 


v 31 3 

2. The gaps. 

2 h 

A ifj-i 

9 \/ fl Q1 Q9 

3. Magnet core. . . 

8 ~3T 


A -rjj- X U.oio/s 

A 2 


v 31 3'> 


ttt A U.OlO/v 
A 3/^3 

If the iron used in armature and core is of the same 
quality, and magnetized up to the same degree of satu- 
ration, //-i and /j-s will be alike. For the air-gaps /j. = 1, 
and therefore is not written in. 

If there were no leakage, the total reluctance would 
simply be the sum of these three terms. But when 
there is leakage, the total reluctance is reduced. 

To calculate the ampere turns of magnetizing power req- 
uisite to force the desired magnetic flux through the 
reluctances of the magnetic circuit, 
(a.) If dimensions are given in centimetres the rulo is: 
Ampere turns = the magnetic flux, multiplied by the 

magnetic reluctance of the circuit, divided by T 4 of n 

(= 1.2566). 


Or, in detail, the three separate amounts of ampere 
turns required for three principal magnetic reluctances 
are explained as follows : 

Ampere turns required to ) 7 A* 

drive N lines through iron > = N X 

of armature ) 

Ampere turns required to ) 07 

drive N lines through the [ = N X - -^ , 

two gaps ) ^2 

Ampere turns required to ) 7 4r 

drive vH lines through the > = vN x ; -, 

iron of magnet core ) ^ 3//3 

And, adding up : 

Total ampere turns re- ( 7 07 7 ^ 

. _ 10 _. 3_A_ + ^!L -H-J^-t. 

quired = N | AM A 2 r A&* \ 

(b.) If dimensions are given in inches, the rule is : 
Ampere turns = magnetic flux multiplied by the 
magnetic reluctance of the circuit. 
Or, in detail : 

Ampere turns required to } ^" 

drive N lines through iron >- = N X-TF~ X 0.3132, 

of armature ) ^ 1/^-1 

Ampere turns required to ) o?// 

drive N lines through two V = N X -~T- X 0.3132. 

gaps ) 

Ampere turns required to ) -^ 

drive vH lines through iron > = vH X nrX 0.3132; 

core of magnet ) -<* V*a 

And, adding up : 

Total ampere turns re- j l"\ 2^2 , vl's ] 

quired = 0.3132N ( ~A\^ Tl 1 ," T 3Va ) ' 


It will be noted that here v, the coefficient of allow- 
ance for leakage, has been introduced. This has to be 
calculated as shown later. In the mean time it may be 
pointed out that, in designing electromagnets for any 
case where v is approximately known beforehand, the 
calculation may be simplified by taking the sectional 
area of the magnet core greater than that of the arma- 
ture in the same proportion. For example, if it were 
known that the waste lines that leak were going to be 
equal in number to those that are usefully employed in 
the armature (here v 2), the iron of the cores might 
be made of double the section of that of the armature. 
In this case // 3 will approximately equal ni. 

To calculate tlie coefficient of allowance for leakage, v. 

v = total magnetic flux generated in magnet core -j- 
useful magnetic flux through armature. The respective 
useful and waste magnetic fluxes are proportional to the 
permeances along their respective paths. Permeance, 
or magnetic conductance, is the reciprocal of the re- 
luctance, or magnetic resistance. Call useful permeance 
through armature and gaps u; and the waste permeance 
in the stray field w; then 

u -f- w 

v = 


w may be estimated by the Table VIII. or other leakage 
rules, but should be divided by 2 as the average differ- 
ence of magnetic potential over the leakage surface is only 
about half that at the ends of the poles. 


(I. to III. adapted from Prof. Forbes 7 rules.) 

Prop. I. Permeance between two parallel areas facing 
one another. Let areas be A\ and A< square inches, 
and distance apart d" inches, then : 

Permeance = 3.193 X i (A'\ + A'*) -r- d". 

Prop. II. Permeance between two equal adjacent rect- 
angular areas lying in one plane. Assuming lines of 
flow to be semicircles, and that distances d" \ and d"% 
between their nearest and furthest edges respectively 
are given, also a" their width along the parallel edge: 

Permeance = 2.274-. X a" X logio^4-- 

Prop. III. Permeance between two equal parallel rect- 
angular areas lying in one plane at some distance apart. 
Assume lines of leakage to be quadrants joined by 
straight lines. 

Permeance = 2.274 X a" X lo glo j 1 + !lilZ^Ll j. 

Prop. IV. Permeance between two equal areas at 
right angles to one another. 

Permeance (if air angle is 90) double the respect- 
ive value calculated by II. or III. 

Permeance (if air angle is 270) = two-thirds times 
the respective value calculated by II. 


If measures are given in centimetres these rules be- 
come the following : 

I. At A + d 


Prop. V. Permeance between two parallel cylinders of 
indefinite length. 

The formula for the reluctance is given above: the 
permeance is the reciprocal of it. Calculations are sim- 
plified by reference to Table VIII. 




IN continuation of my lecture of last week I have to 
make a few remarks before entering upon the consider- 
ation of special forms of magnets which was to form the 
entire topic of to-night's lecture. I had not quite fin- 
ished the experimental results which related to the per- 
formance of magnets under various conditions. I had 
already pointed out that where you require a magnet 
simply for holding on to its armature common sense (in 
the form of our simplest formula) dictated that the cir- 
cuit of iron should be as short as was compatible with 
getting the required amount of winding upon it. That 
at once brings us to the question of the difference in 
performance of long magnets and short ones. Last week 
we treated that topic so far as this, that if you require 
your magnet to attract over any range across an air 
space you require a sufficient amount of exciting power 
in the circulation of electric current to force the mag- 
netic lines across that resistance, and therefore you re- 
quire length of core in order to get the required coil 
wound upon the magnetic circuit. But there is one 


other way in which the difference of behavior between 
long and short magnets I am speaking of horseshoe 
shapes comes, into play. So far back as 1840, Ritchie 
found it was more difficult to magnetize steel magnets 
(using for that purpose electromagnets to stroke them 
with) if those electromagnets were short than if they 
were long. He was of course comparing magnets which 
had the same tractive power, that is to say, presumably 
had the same section of iron magnetized up to the same 
degree of magnetization. This difference between long 
and short cores is obviously to be explained on the same 
principle as the greater projecting power of the long- 
legged magnets. IH order to force magnetism not only 
through an iron arch, but through whatever is beyond, 
which has a lesser permeability for magnetism, whether 
it be an air-gap or an arch of hard steel destined to re- 
tain some of its magnetism, you require magneto-motive 
force enough to drive the magnetism through that re- 
sisting medium; and, therefore, you must have turns of 
wire. That implies that you must have length of leg 
on which to wind those turns. "Ritchie also found that 
the amount of magnetism remaining behind in the soft 
iron arch, after turning off the current at the first re- 
moval of the armature, was a little greater with long 
than with short magnets; and, indeed, it is what we 
should expect now, knowing the properties of iron, that 
long pieces, however soft, retain a little more have a 
little more memory, as it were, of having been magnet- 
ized than short pieces. Later on I shall have specially 
to draw your attention to the behavior of short pieces of 
iron which have no magnetic memory. 



I now take up the question of winding the copper 
wire upon the electromagnet. How are we to determine 
beforehand the amount of wire required and the proper 
gauge of wire to employ ? 

The first stage of such a determination is already ac- 
complished; we are already in possession of the formula 
for reckoning out the number of ampere turns of ex- 
citation required in any given case. It remains to show 
how from this to calculate the amount of bobbin space, 
and the quantity of wire to fill it. Bear in mind that a 
current of 10 amperes (i. e., as strong as that used for a 
big arc light) flowing once around the iron produces 
exactly the same effect magnetically as a current of one 
ampere flowing around ten times, or as a current of 
only one-hundredth part of an ampere flowing around 
a thousand times. In telegraphic work the currents 
ordinarily used in the lines are quite small, usually 
from five to twenty thousandths of an ampere; hence 
in such cases the wire that is wound on need only be a 
thin one, but it must have a great many turns. Be- 
cause it is thin and has a great many turns, and is con- 
sequently a long wire, it will offer a considerable resist- 
ance. That is no advantage, but does not necessarily 
imply any greater waste of energy than if a thicker coil 
of fewer turns were used with a correspondingly larger 
current. Consider a very simple case. Suppose a bob- 
bin is already filled with a certain number of turns of 
wire, say 100, of a size large enough to carry one ampere, 
without overheating. It will offer a certain resistance, 


it will waste a certain amount of the energy of the cur- 
rent, and it will have a certain magnetizing power. 
Now suppose this -bobbin to be rewound with a wire of 
half the diameter; what will the result be ? If the 
wire is half the diameter it will have one-quarter the 
sectional area, and the bobbin will hold four times as 
many turns (assuming insulating materials to occupy 
the same percentage of the available volume). The cur- 
rent which such a wire will carry will be one-fourth as 
great. The coil will offer sixteen times as much resist- 
ance, being four times as long and of one-fourth the 
cross-section of the other wire. But the waste of energy 
will be the same, being proportional to the resistance 
and to the square of the current: for 16 X T V = 1. 
Consequently the heating effect will be the same. Also 
the magnetizing power will be the same, for though the 
current is only one-quarter of an ampere, it flows 
around 400 turns ; the ampere turns are 100, the same 
as before. The same argument would hold good with 
any other numerical instance that might be given. It 
therefore does not matter in the least to the magnetic 
behavior of the electromagnet whether it is wound with 
thick wire or thin wire, provided the thickness of the 
wire corresponds to the current it has to carry, so that 
the same number of watts of power are spent in heating 
it. For a coil wound on a bobbin of given volume the 
magnetizing power is the same for the same heat waste. 
But the heat waste increases in a greater ratio than the 
magnetizing power, if the current in a given coil is in- 
creased; for the heat is proportional to the square of 
the current, and the magnetizing power is simply pro- 


portional to the current. Hence it is the heating effect 
which in reality determines the winding of the wire. 
We muse assuming that the current will have a certain 
strength allow enough volume to admit of our getting 
the requisite number of ampere turns without over- 
heating. A good way is to assume a current of one 
ampere while one calculates out the coil. Having done 
this, the same volume holds good for any other gauge 
of wire appropriate to any other current. The terms 
"long coil" magnet and "short coil" magnet are ap- 
propriate for those electromagnets which have, re- 
spectively, many turns of thin wire and few turns 
of thick wire. These terms are preferable to " high 
resistance" and "low resistance," sometimes used to 
designate the two classes of windings; because, as I 
have just shown, the resistance of a coil has in itself 
nothing to do with its magnetizing power. Given the 
volume occupied by the copper, then for any current 
density (say, for example, a current density of 2,000 
amperes per square inch of cross-section of the copper), 
the magnetizing power of the coil will be the same for 
all different gauges of wire. The specific conductivity 
of the copper itself is of importance; for the better the 
conductivity the less the heat waste per cubic inch of 
winding. High conductivity copper is therefore to be 
preferred in every case. 

Now the heat which is thus generated by the current 
of electricity raises the temperature of the coil (and of 
the core), and it begins to emit heat from its surface. 
It may be taken as a sufficient approximation that a 
single square inch of surface, warmed one degree Fahr, 


above the surrounding air, will steadily emit heat at the 
rate of -g^- of a watt. Or, if there is provided only 
enough surface to allow of a steady emission of heat at 
the rate of one watt l per square inch of surface, the 
temperature of that surface will rise to about 225 de- 
grees Fahr. above the temperature of the surrounding 
air. This number is determined by the average emis- 
sivity of such substances as cotton, silk, varnish, and 
other materials of which the surfaces of coils are usu- 
ally composed. 

In the specifications for dynamo machines it is usual 
to lay down a condition that the coils shall not heat 
more than a certain number of degrees warmer than the 
air. With electromagnets it is a safe rule to say that 
no electromagnet ought ever to heat up to a tempera- 
ture more than 100 degrees Fahr. above the surrounding 
air. In many cases it is quite safe to exceed this limit. 

The resistance of the insulated copper wire on a bob- 
bin may be approximately calculated by the following 
rule. If d is the diameter of the naked wire, in mils, 
and D is the diameter, in mils, of the wire when covered, 
then the resistance per cubic inch of the coil will be: 

.. . , 960,700 
Ohms per cubic inch = 

1 The watt is the unit of rate of expenditure of energy, and is equal to 
ten million ergs per second, or to l-746th of a horse power. A current of one 
ampere, flowing through a resistance of one ohm, spends energy in heating 
at the rate of one watt. One watt is equivalent to 0.24 calories, per second, 
of heat. That is to say, the heat developed in one second, by expenditure of 
energy at the rate of one watt, would suffice to warm one gramme of water 
through 0.24 (Centigrade) degree. As 252 calories are equal to one British 
(pound Fahr.) unit of heat, it follows that heat emitted at the rate of one 
watt would suffice to warm 3.4 pounds of water one degree Fahr. in one hour ; 
or one British unit of heat equals 1,058 watt seconds, 


We are therefore able to construct a wire gauge and 
ampereage table which will enable us to calculate readily 
the degree to which a given coil will warm when tra- 
versed by a given current, or conversely what volume of 
coil will be needed to provide the requisite circulation 
of current without warming beyond any prescribed ex- 

Accordingly, I here give a wire-gauge and ampereage 
table which we have been using for some time at the 
Finsbury Technical College. It was calculated out 
under my instructions by one of the demonstrators of 
the college, Mr. Eustace Thomas, to whom I am in- 
debted for the great care bestowed upon the calculations 

For many purposes, such as for use in telegraphs and 
electric bells, smaller wires than any of those mentioned 
in the table are required. The table is, in fact, intei: ! 
for use in calculating .n gnets in larger engineer!, 

A rough-and-ready rule sometimes given for the size 
of wire is to allow T oVo square inch per ampere. This 
is an absurd rule, however, as the figures in the table 
show. Under the heading 1,000 amperes to square inch, 
it appears tha^ if a No. 18 S. W. G. wire is used it will 
at that rate carry 1.81 amperes; that if there is only 
one layer of wire, it will only warm up 4.G4 degrees 
Fahr., consequently one might wind layer after layer to 
a depth of 3.3 inches, without getting up to the limit of 
allowing one square inch per watt for the emission of 
heat. In very few cases does one want to wind a coil so 
thick as 3.3 inches. For very few electromagnets is it 
needful that the layer of coil exceed half an inch in 



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thickness; and if the layer is going to be only half an 
inch thick, or about one-seventh of the 3.3, one may 
use a current density A/7 times as great as 1,000 am- 
peres per square inch, without exceeding the limit of 
safe working. Indeed, with coils only half an inch 
thick, one may safely employ a current density of 3,000 
amperes per square inch, owing to the assistance which 
the core gives for the dissipation and emission of heat. 
Suppose, then, we have designed a horseshoe magnet, 
with a core one inch in diameter, and that, after con- 
sidering the work it has to do, it is found that a mag- 
netizing power of 2,400 turns is required; suppose, also, 

Figures in columns marked A signify number of amperes that the wire 

Figures in columns marked F signify number of degrees (Fahrenheit) 
that the coil will warm up if there is only one layer of w r ire, and on the 
assumption that the heat is radiated only from the outer surface of the 
coil ; they are calculated by the following modification of Forbes 1 rule : 

Rise in temperature (Fahrenheit deg.) = 225 x No. of watts lost per sq. inch. 

= 159 x sectional area X number of 
turns to one inch (at 1,000 amps, 
per sq. inch). 

Figures in columns marked D are the depth in inches to which wire may 
be wound if one watt be lost by each square inch of radiating surface, the 
outside radiating surface of the bobbin being only considered. 

Rule for calculating a 7-strand cable: Diatn. of cable = 1.134 X diam. of 
equivalent round wire. 

Figures under heading "Turns to one linear inch 11 are calculated for 
cotton covered wires of average thicknesses of coverings used for the dif- 
ferent gauges, viz., 14 mils additional diameter on round wires (from No. 22) 
and 20 mils on stranded or square wire. 

Figures under heading "Turns per square inch 11 are calculated from 
preceding, allowing 10 per cent, for bedding of layers. 

Resistance (ohms) of coil of copper wire, occupying v cubic inches of coil 
space, and of which the gauge is d mils uncovered, and D mils covered, may 
be approximately calculated by the rule : 

ohms = 960,700^ 

The data respecting sizes of wires of various gauges are kindly furnished by 
the London Electric Wire Company. 


that it is laid down as a condition that the coil 
must not warm up more than 50 degrees Fahr. above 
the surrounding air what volume of coil will be re- 
quired ? Assume, first, that the current will be one 
ampere; then there will have to be 2,400 turns of a 
wire which will carry one ampere. If we took a No. 
20 S. W. G. wire and wound it to the depth of half an 
inch, that would give 220 turns per inch length of coil; 
so that a coil 11 inches long and a little over half an 
inch deep (or ten layers deep) would give 2,400 turns. 
Now Table X. shows that if this wire were to carry 
1.018 amperes it would heat up 225 degrees Fahr. if 
wound to a depth of 3.9 inches. If wound to half an 
inch, it would therefore heat up about 30 degrees Fahr.; 
and with only one ampere would, of course, heat less. 
This is too good; try the next thinner wire. No. 22 S. 
W. G. wire at 2,000 amperes to the square inch will 
carry 1.23 amperes, and heats 225 degrees if wound up 
1.13 inches. If it is only to heat 50 degrees, it must 
not be wound more than one-fourth inch deep; but if 
it only carries current of one ampere it may be wound 
a little deeper say to 14 layers. There will then be 
wanted a coil about seven inches long to hold the 2,400 
turns. The wire will occupy about 3.85 square inches 
of total cross-section, and the volume of the space oc- 
cupied by the winding will be 26.95 cubic inches. Two 
bobbins, each 3| inches long and .65 deep, to allow for 
14 layers, will be suitable to receive the coils. 

By the light of the knowledge one possesses as to the 
relation between emissivity of surface, rate of heating 
by current, and limiting temperatures, it is seen how 


little justification there is for such empirical rules cs 
that which is often given, namely, to make the depth 
of coil equal to the diameter of the iron core. Consider 
this in relation to the following fact ; that in all those 
cases where leakage is negligible the number of ampere- 
turns that will magnetize up a thin core to any pre- 
scribed degree of magnetization will magnetize up a 
core of any section whatever, and of the same length, to 
the same degree of magnetization. A rule that would 
increase the depth of copper proportionately to the 
diameter of ':he iron core is absurd. 

Where less accurate approximations are all that is 
needed, more simple rules can be given. Here are two 
cases : 

Case 1. Lea/cage assumed to be negligible. Assume 
B = 16,000, then H = 50 (see Table III.). Hence the 
ampere turns per centimetre of iron will have to be 40, 
or per inch of iron 102; for H is equal to 1.2566 times 
the ampere turns per centimetre. Now, if the winding 
is not going to exceed one-half inch in depth, we may 
allow 4,000 amperes per square inch without serious 
overheating. And the 4,000 ampere turns will require 
2-inch length of coil, or each inch of coil carries 2,000 
ampere turns without overheating. Hence each inch 
of coil one-half inch deep will suffice to magnetize up 
20 inches length of iron to the prescribed degree. 

Case 2. Leakage assumed to be 50 per cent. Assume 
B in air-gap = H = 8,000, then to force this across re- 
quires ampere turns 6,400 per centimetre of air, or 16,- 
250 per inch of air. Now, if winding is not going to 
exceed one-half inch depth, each inch length of coil will 


carry 2,000 ampere tu A Hence, eight inches length 
of coil one-quarter inch deep will be required for one 
inch length of air, magnetized up to the prescribed de- 


In winding coils for magnets that are to be used on 
any electric light system, it should be carefully borne 
in mind that there are separate rules to be considered 
according to the nature of the supply. If the electric 
supply is at constant pressure, as usual for glow lamps, 
the winding of coils of electromagnets follows the same 
rule as the coils of voltmeters. If the supply is with 
constant current, as usual for arc lighting in series, then 
the coils must be wound with due regard to the current 
which the wire will carry, when lying in layers of suita- 
ble thickness, the number of turns being in this case the 
same whether thin or thick wire is used. 

If we assume that a safe limit of temperature is 90 
degrees Fahr. higher than the surrounding air, then the 
largest current which may be used with a given electro- 
magnet is expressed by the formula: 

Highest permissible amperes = 0.63 V - 

where s is the number of square inches of surface of 
the coils and r their resistance in ohms. 

Similarly for coils to be used as shunts we have: 

Highest permissible volts = 0.63 V sr 


The magnetizing power of a coil, supplied at a given 
number of volts of pressure, is independent of its length, 
and depends only on its gauge, but the longer the wire 
the less will be the heat waste. On the contrary, when 
the condition of supply is with a constant number of 
amperes of current, the magnetizing power of a coil is 
independent of the gauge of the wire, and depends only 
on its length; but the larger the gauge the less will be 
the heat waste. 


To reach the same limiting temperature with bobbins 
of equal size, wound with wires of different gauge, the 
cross-section of the wire must vary with the current it 
is to carry; or, in other words, the current density 
(amperes per square inch) must be the same in each. 
Table X. shows the ampereages of the various sizes of 
wires at four different values of current density. 

To raise to the same temperature two similarly shaped 
coils, differing in size only, and having the gauges of 
the wires in the same ratio (so that there are the same 
number of turns on the large coil as on the small one), 
the currents must be proportional to the square roots of 
the cubes of the linear dimensions. 

Sir William Thomson has given a useful rule for cal- 
culating windings of electromagnets of the same type 
but of different sizes. Similar iron cores, similarly 
wound with lengths of wire proportional to the squares 
of their linear dimensions, will, when excited with equal 
currents, produce equal intensities of magnetic field at 
points similarly situated with respect to them. 


Similar electromagnets of different sizes must have 
ampere turns proportional to their linear dimensions if 
they are to be magnetized up to an equal degree of sat- 

It is curious what erroneous notions crop up from 
time to time about winding electromagnets. In 1869 
a certain Mr. Lyttle took out a patent for winding the 
coils in the following way: Wind the first layer as 
usual, then bring the wire back to the end where the 
winding began and wind a second layer, and so on. In 
this way all the windings will be right-handed, or else 
all left-handed, not alternately right and left as in the 
ordinary winding. Lyttle declared that this method of 
winding a coil gave more powerful effects; so did M. 
Brisson, who reinvented the same mode of winding in 
1873, and solemnly described it. Its alleged superiority 
was at once disproved by Mr. W. H. Preece, who 
found the only difference to be that there was more 
difficulty in carrying out this mode of winding. 

Another popular error is that electromagnets in which 
the wires are badly insulated are more powerful than 
those in which they are well insulated. This arises 
from the ignorant use of electromagnets having long, 
thin coils (of high resistance) with batteries consisting 
of a few cells (of low electromotive force). In such 
cases, if some of the coils are short circuited, more cur- 
rent flows, and the magnetizing power may be greater. 
But the scientific cure is either to rewind the magnet 
with an appropriate coil of thick wire, or else to apply 
another battery having an electromotive force that is 



One frequently comes across specifications for con- 
struction which prescribe that an electromagnet shall be 
wound so that its coil shall have a certain resistance. 
This is an absurdity. Eesistance does not help to 'mag- 
netize the core. A better way of prescribing the wind- 
ing is to name the ampere turns and the temperature 
limit of heating. Another way is to prescribe the num- 
ber of watts of energy which the magnet is to take. 
Indeed, it would be well if electricians could agree upon 
some sort of figure of merit by which to compare elec- 
tromagnets, which should take into account the magnetic 
output L e., the product of magnetic flux into magneto- 
motive force the consumption of energy in watts, the 
temperature rise, and the like. 


In dealing with this question of winding copper on a 
magnet core, I cannot desist from referring to that rule 
which is so often given, which I often wish might dis- 
appear from our text-books the rule which tells you in 
effect that you are to waste 50 per cent, of the energy 
you employ. I refer to the rule which states that you 
will get the maximum effect out of an electromagnet if 
you so wind it that the resistance is equal to the resist- 
ance of the battery you employ; or that if you have a 
magnet of a given resistance you ought to employ a 
battery of the same resistance. "What is the meaning of 
this rule ? It is a rule which is absolutely meaningless, 


unless in the first case the volume of the coil is pre- 
scribed once for all, and you cannot alter it; or unless 
once for all the number of battery elements that you 
can have is prescribed. If you have to deal with a fixed 
number of battery elements, and you have to get out 
of them the biggest effect in your external circuit, and 
cannot beg, buy, or borrow any more cells, it is per- 
fectly true that, for steady currents, you ought to group 
them so that their internal resistance is equal to the 
external resistance that they have to work through; and 
then, as a matter of fact, half the energy of the battery 
will be wasted, but the output will be a maximum. Now 
that is a very nice rule indeed for amateurs, because an 
amateur generally starts with the notion that he does 
not want to economize in his rate of working; it does 
not matter whether the battery is working away furi- 
ously, heating itself, and wasting a lot of power; all he 
wants is to have the biggest possible effect for a little 
time out of the fewest cells. It is purely an amateur's 
rule, therefore, about equating the resistance inside to 
the resistance outside. But it is absolutely fallacious to 
set up any such rule for serious working; and not only 
fallacious, but absolutely untrue if you are going to deal 
with currents that are going to be turned off and on 
quickly. For any apparatus like an electric bell, or 
rapid telegraph, or induction coil, or any of those 
things where the current is going to vary up and down 
rapidly, it is a false rule, as we shall see presently. 
What is the real point of view from which one ought to 
start ? I am often asked questions by, shall I say, ama- 
teurs, as well as by those who are not amateurs, about 


prescribing the battery for a given electromagnet, or 
prescribing an electromagnet for a given battery. Again, 
I am often told of cases of failure, in which a very little 
common sense rightly directed might have made a suc- 
cess. What one ought to think about in every case is 
not the battery, not the electromagnet, but the line. 
If you have a line, then you must have a battery and 
electromagnet to correspond. If the line is short and 
thick, a few feet of good copper wire, you should have 
a short, thick battery, a few big cells or one big cell, and 
a short, thick coil on your electromagnet. If you have 
a long, thin line, miles of ft, say, you want a long, thin 
battery (small cells, and a long row of them) and a long, 
thin coil. That is then our rule : for a short, thick line, 
a short, thick battery and a short, thick coil; for a long, 
thin line, a long, thin battery and electromagnet coils 
to match. You smile; but it is a really good rule that 
I am giving you; vastly better than the worn-out ama- 
teur rule. 

But, after all, my rule does not settle the whole ques- 
tion, because there is something more than the whole 
resistance of the circuit to be taken into account. 
Whenever you come to rapidly acting apparatus, you 
have to think of the fact that the current, while vary- 
ing, is governed not so much by the resistance as by 
the inertia of the circuit its electromagnetic inertia. 
As this is a matter which will claim our especial atten- 
tion hereafter, I will leave battery rules for the present 
and proceed with the question of design. 



This at once leads us to consider the classification of 
forms of magnets. I do not pretend to have found a 
complete classification. There is a very singular book 
written by Monsieur Nickles, in which he classifies under 
37 different heads all conceivable kinds of magnets, 
bidromic, tridromic, monocnemic, multidromic, and I 
do not know how many more; but the classification is 
both unmeaning and unmanageable. For my present 
purpose I will simply pick out those which come under 
three or four heads, and deal separately with others that 
do not quite fit under any of the four categories. 

Bar Electromagnets. In the first place there are those 
which have a straight core, of which there are several 
specimens on the table here. 

Horseshoe Electromagnets. Then there are the horse- 
shoes, of which some are of one piece, bent, and others 
here of the more frequent shape, made of three pieces. 

Iron-clad Electromagnets. Then from the horseshoes 
I go to those magnets in which the return circuit of the 
iron comes back outside the coil from one end or the 
other, or from both ends, sometimes in the form of an 
external tube or jacket, sometimes merely with a parallel 
return yoke, or two parallel return yokes. All such 
magnets I propose to call following the fashion that 
has been adopted for dynamos iron-clad electromagnets. 
One of them, the jacketed electromagnet, is shown in 
Fig. 12, and there are others not so well known. There 
is one used by Mr. Cromwell Varley, in which a straight 
magnet is placed between a couple of iron caps, which 


fit over the ends, and virtually bring the poles down 
close together, the circular rim of one cap being the 
north pole and that of the other cap being the south 
pole, the two rims being close together. That plan, of 
course, produces a great tendency to leak across from 
one rim to the other all round. The advantages, as 
well as the disadvantages, of the jacketed magnet I 
alluded to in my last lecture, when I pointed out to you 
that for all action at a distance it is far better not to 
have an iron-clad return 
path, whereas for action in 
contact the iron-clad magnet 
was distinctly a very good 
form. In one form of iron- 
clad magnet the end of the 
straight central core is fixed 
to the middle of a bar of ^ ^ 1 i- 1 

iron, the ends Of which are FIG. 50.- CLUB-FOOTED ELECTRO- 

bent up and brought flush 

with the top of the bobbin, making thus a tripolar 
magnet, with one pole between the other two. The 
armature in this form is a bar which lies right across 
the three poles. There is an example of this excellent 
kind of electromagnet applied in one of the forms of 
electric bell indicator made by Messrs. Gent, of Leicester. 
Then besides these three main classes the straight 
bar, the horseshoe, and the iron-clad there is another 
form which is so useful and so commonly employed in 
certain work that it deserves to have a name of its own. 
It is that called by Count Du Moncel iheaimant boiteux, 
or club-footed magnet (Fig. 50). It is a horseshoe, in 


fact, with a coil upon one pole and no coil upon the 
other. The advantage of that construction is simply, I 
suppose, that you will save labor you will only have to 
wind the wire on one pole instead of two. Whether 
that is an improvement in any other sense is a question 
for experiment to determine, but on which theory per- 
haps might now be able to say something. Count Du 
Moncel, who made many experiments on this form of 
magnet, ascertained that there was for an equal weight 
of copper a slight falling off in power with the club- 
footed magnet. Indeed, one might almost predict, for 
a given weight of copper, if you wound all in one coil 
only, you will not make as many turns as if you wound 
it in two, the outer turns on the coil being so much 
larger than the average turn when wound in two coils. 
Consequently the number of ampere turns with a given 
weight of copper would be rather smaller, and you would 
require more current to bring the magnetizing power 
up to the same value as with the two coils. At the same 
time the one coil may be produced a little more cheaply 
than the two; and indeed such electromagnets are really 
quite common, being largely used for the sake of cheap- 
ness and compactness in indicators or electric bells. 

Du Moncel tried various experiments about this form 
to find whether it acted better when the armature was 
pivoted over one pole or over the other, and found it 
worked best when the armature was actually hinged on 
to that pole which comes up through the coil. He made 
two experiments, trying coils on one or the other limb, 
the armature being in each case set at an equal distance. 
In one experiment he found the pull was 35 grammes, 


with an armature hinged on to the idle pole, and 40 
grammes when it was hinged on to the pole which car- 
ried the coil. 

Another form of electromagnet, having but one coil, 
is used in the electric bells of church-bell pattern, of 
which Mr. H. Jensen is the designer. In Jensen's elec- 
tromagnet a straight cylindrical core receives the bob- 
bin for the coil, and, after this has been pushed into its 
place, two ovate pole-pieces are screwed upon its ends, 
serving thus to bring the magnetic circuit across the 
ends of the bobbin, and forming a magnetic gap along 
the side of the bobbin. The armature is a rectangular 
strip of soft iron, about the same length as the core, and 
is attracted at one end by one pole-piece and at the 
other end by the other. 


Seeing that the magnetizing power which a coil ex- 
erts on the magnetic circuit which it surrounds is sim- 
ply proportional to the ampere turns, it follows that 
those turns which lie on the outside layers of the coil, 
though they are further away from the iron core, pos- 
sess precisely equal magnetizing power. This is strictly 
true for all closed magnetic circuits; but in those open 
magnetic circuits where leakage occurs it is only true 
for those coils which encircle the leakage lines also. For 
example, in a short bar electromagnet, of the wide 
turns on the outer layer, those which encircle the mid- 
dle part of the bar do inclose all the magnetic lines, and 
are just as operative as the smaller turns that underlie 
them ; while those wide turns which encircle the end 


portions of the bur are not so efficient, as some of the 
magnetic lines leak back past these coils. 


Among the other researches which Du Moncel made 
with respect to electromagnets was one on the best posi- 
tion for placing the coil upon the iron core. This is a 
matter that other experimenters have examined. In 
Dub's book, "Elektromagnetismus," to which I have 
several times referred, you will also find many experi- 
ments on the best position of a coil; but it is perhaps 
sufficient to narrate a single example. Du Moncel had 
four pairs of bobbins made of exactly the same volume, 
and with 50 metres of wire on each ; one pair was 16 
centimetres long, another pair eight centimetres, or half 
the length, with not quite so many turns, because of 
course the diameter of the outer turn was larger, one 
four centimetres in length and another two centime- 
tres. These were tried both with bar magnets and 
horseshoes. It will suffice, perhaps, to give the result 
of the horseshoe. The horseshoe was made long enough 
16 centimetres only, a little over six inches long to 
carry the longest coil. Now when the compact coils 
two centimetres long were used, the pull on the arma- 
ture at a distance away of two millimetres (it was al- 
ways the same, of course, in the experiments) was 40 
grammes. Using the same weight of wire, but distrib- 
uted on the coils twice as long, the pull was 55 grammes. 
Using the coils eight centimetres long it was 75 grammes, 
and using the coils 16 centimetres long, covering the 
length of each limb, the pull was 85, clearly showing 


that, where you have a given length of iron, the best 
way of winding a magnet to make it pull with its great- 
est pull is not to heap the coil up against the poles, but 
to wind it uniformly; for this mode of winding will give 
you more turns, therefore more ampere turns, therefore 
more magnetization. An exception might, however, 
occur in some case where there is a large percentage of 
leakage. With club-footed magnets results of the same 
kind are obtained. It was found in every case that it 
was well to distribute the coil as much as possible along 
the length of the limb. All these experiments were 
made with a steady current. It does not follow, how- 
ever, because winding the wire over the whole length of 
core is best for steady currents that it is the best wind- 
ing in the case of a rapidly varying current; indeed, we 
shall see that it is not. 


So far as the carrying capacity for magnetic lines is 
concerned, one shape of section of cores is as good as 
another; square or rectangular is as good as round if 
containing equal sectional area. But there are two 
other reasons, both of which tell in favor of round cores. 
First, the leakage of magnetic lines from core to core is, 
for equal mean distances apart, proportional to the sur- 
face of the core; and the round core has less surface 
than square or rectangular of equal section. All edges 
and corners, moreover, promote leakage. Secondly, the 
quantity of copper wire that is required for each turn 
will be less for round cores than for cores any other 


shape, for of all geometrical figures of equal area the 
circle is the one of the least periphery. 


Another matter that Du Moncel experimented upon, 
and Dub and Nickles likewise, was the distance between 
the poles. Dub considered that it made no difference 
how far the poles were apart. Nickles had a special ar- 
rangement made which permitted him to move the two 
upright cores or limbs, nine centimetres high, to and 
fro on a solid bench or yoke of iron. His armature was 
30 centimetres long. Using very weak currents, he 
found the effect best when the shortest distance be- 
tween the poles was three centimetres; with a stronger 
current, 12 centimetres; and with his strongest current, 
nearly 30 centimetres. I think leakage must have a 
deal to do with these results. Du Moncel tried various 
experiments to elucidate this matter, and so did Prof. 
Hughes in an important but too little known re- 
search, which came out in the Annales Telegraphiques 
in the year 1862. 


His object was to find out the best form of electro- 
magnet, the best distance between the poles, and the 
best form of armature for the rapid work required in 
Hughes' printing telegraphs. One word about Hughes' 
magnet. This diagram (Fig. 51) shows the form of 
the well known Hughes electromagnet. 1 feel almost 
ashamed to say those words "well known," because al- 
though on the Continent everybody knows what you 



mean by a Hughes electromagnet, in England scarcely 
any one knows what you mean. Englishmen do not 
even know that Prof. Hughes has invented a special 
form of electromagnet. Hughes' special form is this : 
A permanent steel magnet, generally a compound one, 
having soft iron pole-pieces, and a couple of coils on the 
pole-pieces only. As I have to speak of Hughes' spe- 
cial contrivance among the mechanisms that will oc- 


cupy our attention next week, I only now refer to this 
magnet in one particular. If you wish a magnet to 
work rapidly, you will secure the most rapid action, not 
when the coils are distributed all along, but when they 
are heaped up near, not necessarily entirely on, the 
poles. Hughes made a number of researches to find out 
what the right length and thickness of these pole-pieces 
should be. It was found an advantage not to use too 
thin pole-pieces, otherwise the magnetism from the per- 


manent magnet did not pass through the iron without 
considerable reluctance, being choked by insufficiency 
of section; also not to use too thick pieces, otherwise 
they presented too much surface for leakage across from 
one to the other. Eventually a particular length was 
settled upon, in proportion about six times the diame- 
ter, or rather longer. In the further researches that 
Hughes made he used a magnet of shorter form, not 
shown here, more like those employed in relays, and 
with an armature from two to three millimetres thick, 
one centimetre wide, and five centimetres long. The 
poles were turned over at the top toward one another. 
Hughes tried whether there was any advantage 
in making those poles approach one another, and 
whether there was any advantage in having as long an 
armature as five centimetres. He tried all different 
kinds, and plotted out the results of observations in 
curves, which could be compared and studied. His ob- 
ject was to ascertain the conditions which would give 
the strongest pull, not with a steady current, but with 
such currents as were required for operating his print- 
ing telegraph instruments ; currents which lasted only 
from one to twenty hundredths of a second. He found 
it was decidedly an advantage to shorten the length of 
the armature, so that it did not protrude far over the 
poles. In fact, he got a sufficient magnetic circuit to 
secure all the attractive power that he needed, without 
allowing as much chance of leakage as there would have 
been had the armature extended a longer distance over 
the poles. He also tried various forms of armature 
having very various cross-sections, 



In one of Du MonceFs papers on electromagnets 2 you 
will also find a discussion on armatures, and the best 
forms for working in different positions. Among 
other things in Du Moncel you will find this paradox ; 
that whereas, using a horseshoe magnet with flat poles, 
and a flat piece of soft iron for armature, it sticks on 
far tighter when put on edgewise, on the other hand, 
if you are going to work at a distance, across air, the 
attraction is far greater when it is set flatwise. I 
explained the advantage of narrowing the surfaces of 
contact by the law of traction, B 2 coming in. Why 
should we have for an action at a distance the greater 
advantage from placing the armature flatwise to the 
poles? It is simply that you thereby reduce the reluc-\ f\ J^\ 
tance offered by the air-gap to the flow of the magnetic ' 
lines. Du Moncel also tried the difference between ) fj/' 
round armatures and flat ones, and found that a cylin- 
drical armature was only attracted about half as strongly $** 
as a prismatic armature having the same surface when 
at the same distance. Let us examine this fact in the 
light of the magnetic circuit. The poles are flat. You 
have at a certain distance away a round armature ; there 
is a certain distance between its nearest side and the 
polar surfaces. If you have at the same distance away 
a flat armature having the same surface, and, therefore, 
about the same tendency to leak, why do you get a 
greater pull in this case than in that ? I think it is 
clear that, if they are at the same distance away, giving 

2 La Lumiere Electrique, vol. ii. 


the same range of motion, there is a greater magnetic 
reluctance in the case of the round armature, although 
there is the same periphery, because though the nearest 
part of the surface is at the prescribed distance, the rest 
of the under surface is farther away, so that the gain 
found in substituting an armature with a flat surface is 
a gain resulting from the diminution in the resistance 
offered by the air-gap. 


Another of Du Moncel's researches 3 relates to the 
effect of polar projections or shoes movable pole-pieces, 
if you like upon a horseshoe electromagnet. The core 
of this magnet was of round iron four centimetres in 
diameter, and the parallel limbs were ten centimetres 
long and six centimetres apart. The shoes consisted of 
two flat pieces of iron slotted out at one end, so that 
they could be slid along over the poles and brought 
nearer together. The attraction exerted on a flat arma- 
ture across air-gaps two millimetres thick was measured 
by counterpoising. Exciting this electromagnet with a 
certain battery, it was found that the attraction was 
greatest when the shoes were pushed to about 15 milli- 
metres, or about one-quarter of the inter-polar distance, 
apart. The numbers were as follows: 

Distance between 

shoes. Attraction, 

Millimetres. in grammes. 

2 900 

10 1,012 

15 1,025 

25 965 

40 890 

60 550 

_ _i_ . . . . . 

8 La Lumiere Electrique, vol. iv., p. 129. 


With, a stronger battery the magnet without shoes 
had an attraction of 885 grammes, but with the shoes 15 
millimetres apart, 1,195 grammes. When one pole only 
was employed, the attraction, which was 88 grammes 
without a shoe, was diminished by adding a shoe to 39 
grammes ! 


Now, I want particularly to ask you to guard against 
the idea that all these results obtained from electro- 
magnets are equally applicable to permanent magnets 
of steel; they are not, for this simple reason. With 
an electromagnet, when you put the armature near, and 
make the magnetic circuit better, you not only get more 
magnetic lines going through that armature, but you 
get more magnetic lines going through the whole of the 
iron. You get more magnetic lines round the bend 
when you put an armature on to the poles, because you 
have a magnetic circuit of less reluctance, with the same 
external magnetizing power in the coils acting around 
it. Therefore, in that case, you will have a greater mag- 
netic flux all the way round. The data obtained with 
the electromagnet (Fig. 43), with the exploring coil C 
on the bend of the core, when the armature was in con- 
tact and when it was removed, are most significant. 
When the armature was present it multiplied the total 
magnetic flow tenfold for weak currents and nearly 
threefold for strong currents. But with a steel horse- 
shoe, magnetized once for all, the magnetic lines that 
flow around the bend of the steel are a fixed quantity, 



and, however much you diminish the reluctance of the 
magnetic circuit, you do not create or evoke any more. 
When the armature is away the magnetic lines arch 
across, not at the ends of the horseshoe only, but from 
its flanks, the whole of the magnetic lines leaking some- 
how across the space. When you have put the armature 
x- on, these lines, instead of 
arching out into space as 
freely as they did, pass for 
the most part along the steel 
limbs and through the iron arma- 
ture*. You may still have a con- 
siderable amount of leakage, but 
you have not made one line more go 
through the bent part. You have 
absolutely the same number going 
through the bend with the arma- 
ture off as with the armature on. 
You do not add to the total num- 
ber by reducing the magnetic re- 
luctance, because you are not work- 

FIG.52.-EXPERIMENTWITH ^ *i nnuence O f a 


constantly impressed magnetizing 
force. By putting the armature on to a steel horseshoe 
magnet you only colled the magnetic lines, you do not 
multiply them. This is not a matter of conjecture. 
A group of my students have been making experiments 
in the following way : They took this large steel horse- 
shoe magnet (Fig. 52), the length of which from end to 
end through the steel is 42^ inches. A light narrow 
frame was constructed, so that it could be slipped on 


over the magnet, and on it were wound 30 turns of fine 
wire, to serve as an exploring coil. The ends of this 
coil were carried to a distant part of the laboratory, and 
connected to a sensitive ballistic galvanometer. The 
mode of experimenting is as follows : The coil is slipped 
on over the magnet (or over its armature) to any desired 
position. The armature of the magnet is placed gently 
upon the poles, and time enough is allowed to elapse 
for the galvanometer needle to settle to zero. The 
armature is then suddenly detached. The first SAving 
measures the change, due to removing the armature, in 
the number of magnetic lines that pass through the 
coil in the particular position. 

I will roughly repeat the experiment before you; the 
spot of light on the screen is reflected from my galva- 
nometer at the far end of the table. I place the explor- 
ing coil just over the pole, and slide on the armature ; 
then close the galvanometer circuit. Now I detach the 
armature, and you observe the large swing. I shift the 
exploring coil, right up to the bend; replace the arma- 
ture; wait until the spot of light is brought to rest at 
the zero of the scale. Now, on detaching the armature, 
the movement of the spot of light is quite impercepti- 
ble. In our careful laboratory experiments the effect 
was noticed inch by inch all along the magnet. The 
effect when the exploring coil was over the bend was 
not as great as l-3000th part of the effect when the coil 
.was hard up to the pole. We are therefore justified in 
saying that the number of magnetic lines in a perma- 
nently magnetized steel horseshoe magnet is not altered 
by the presence or absence of the armature. 


You will have noticed that I always put on the arma- 
ture gently. It does not do to slam on the armature ; 
every time you do so you knock some of the so-called 
permanent magnetism out of it. But you may pull off 
the armature as suddenly as you like. It does the mag- 
net good rather than harm. There is a popular super- 
stition that you ought never to pull off the keeper of a 
magnet suddenly. On investigation, it is found that 
the facts are just the other way. You may pull off the 
keeper as suddenly as you like; but you should never 
slam it on. 

From these experimental results I pass to the special 
design of electromagnets for special purposes. 


These have already been dealt with in the preceding 
lecture, the characteristic feature of all the forms suit- 
able for traction being the compact magnetic circuit. 

Several times it has been proposed to increase the 
power of electromagnets by constructing them with in- 
termediate masses of iron between the central core and 
the outside, between the layers of windings. All these 
constructions are founded on fallacies. Such iron is far 
better placed either right inside the coils or right out- 
side them, so that it may properly constitute a part of 
the magnetic circuit. The constructions known as 
Oamacho's and Cancels, and one patented by Mr. S. A. 
Varley in 1877, belonging to this delusive order of ideas, 
are now entirely obsolete. 

Another construction which is periodically brought 
forward as a novelty is the use of iron windings of wire 


or strip in place of copper winding. The lower elec- 
tric conductivity of iron, as compared with copper, 
makes such a construction wasteful of exciting power. 
To apply equal magnetizing power by means of an iron 
coil implies the expenditure of about six times as many 
watts as need be expended if the coil is of copper. 


We have already laid down the principle which will 
enable us to design electromagnets to act at a distance. 
We want our magnet to project, as it were, its force 
across the greatest length of air-gap. Clearly, then, 
such a magnet must have a very large magnetizing 
power, with many ampere turns upon it, to be able to 
make the required number of magnetic lines pass across 
the air resistance. Also it is clear that the poles must 
not be too close together for its work, otherwise the 
magnetic lines at one pole will be likely to coil round 
and take short cuts to the other pole. There must be a 
wider width between the poles than is desirable in elec- 
tromagnets for traction. 


In designing an apparatus to put on board a boat or 
a balloon, where weight is a consideration of primary 
importance, there is again a difference. There are three 
things that come into play iron, copper, and electric 
current. The current weighs nothing; therefore if you 
are going to sacrifice everything else to weight, you may 
have comparatively little iron; but you must have 


enough copper to be able to carry the electric current; 
and under such circumstances you must not mind heat- 
ing your wires nearly red hot to pass the biggest possi- 
ble current. Provide as little copper as you conveniently 
can, sacrificing economy in that case to the attainment 
of your object; but, of course, you must use fire-proof 
material, such as asbestos, for insulating, instead of cot- 
ton or silk. 


In all cases of design there is one leading principle 
which will be found of great assistance; namely, that a 
magnet always tends so to act as though it tried to 
diminish the length of its magnetic circuit. It tries to 
grow more compact. This is the reverse of that which 
holds good with an electric current. The electric cir- 
cuit always tries to enlarge itself, so as to inclose as 
much space as possible, but the magnetic circuit always 
tries to make itself as compact as possible. Armatures 
are drawn in as near as can be, to close up the magnetic 
circuit. Many two-pole electromagnets show a tendency 
to bend together when the current is turned on. One 
form in particular, which was devised by Ruhmkorff for 
the purpose of repeating Faraday's celebrated experi- 
ment on the magnetic rotation of polarized light, is 
liable to this defect. Indeed, this form of electromag- 
net is often designed very badly, the yoke being too 
thin, both mechanically and magnetically, for the pur- 
pose which it has to fulfill. 

Here is a small electric bell, constructed by Wagener, 
of Wiesbaden, the construction of which illustrates this 


principle. The electromagnet, a horseshoe,, lies horizon- 
tally; its poles are provided with protruding, curved 
pins of brass. Through the armature are drilled two 
holes, so that it can be hung upon the two brass pins, 
and when so hung up it touches the ends of the iron 
cores just at one edge, being held from more perfect 
contact by a spring. There is no complete gap, there- 
fore, in the magnetic circuit. When the current comes 
and applies a magnetizing power it finds the magnetic 


circuit already complete in the sense that there are no 
absolute gaps. But the circuit can be bettered by tilt- 
ing the armature to bring it flat against the polar ends, 
that being indeed the mode of motion. This is a most 
reliable and sensitive pattern of bell. 

Electromagnetic Pop-Gun. Here is another curious 
illustration of the tendency to complete the magnetic 
circuit. Here is a tubular electromagnet (Fig. 53), con- 
sisting of a small bobbin, the core of which is an iron 
tube about two inches loDg. There is nothing very un- 


usual about it; it will stick on, as you see, to pieces of 
iron when the current is turned on. It clearly is an 
ordinary electromagnet in that respect. Now, suppose 
I take a little round rod of iron, about an inch long, and 
put it into the end of the tube, what will happen when 
I turn on my current ? In this apparatus as it stands 
the magnetic circuit consists of a short length of iron, 
and then all the rest is air. The magnetic circuit will 
try to complete itself, not by shortening the iron, but 
by lengthening it; by pushing the piece of iron out so 
as to afford more surface for leakage. That is exactly 
what happens; for, as you see, when I turn on the cur- 
rent the little piece of iron shoots out and drops down. 
You see that little piece of iron shoot out with consid- 
erable force. It becomes a sort of magnetic pop-gun. 
This is an experiment which has been twice discovered. 
I found it first described by Count Du Moncel, in the 
pages of La Lumiere Electrique, under the name of the 
"pistolet electromagnetique;" and Mr. Shelf ord Bid- 
well invented it independently. I am indebted to him 
for the use of this apparatus. He gave an account of it 
to the Physical Society in 1885, but the reporter missed 
it, I suppose, as there is no record in the society's pro- 


When you are designing electromagnets for use with 
alternating currents, it is necessary to make a change 
in one respect, namely, you must so laminate the iron 
that internal eddy currents shall not occur; indeed, for 


all rapid acting electromagnetic apparatus it is a good 
rule that the iron must not be solid. It is not usual 
with telegraphic instruments to laminate them by mak- 
ing up the core of bundles of iron plates or wires, but 
they are often made with tubular cores ; that is to say, 
the cylindrical iron core is drilled with a hole down the 
middle, and the tube so formed is slit with a saw-cut to 
prevent the circulation of currents in the substance of 
the tube. Now, when electromagnets are to be employed 
with rapidly alternating currents, such as are used for 
electric lighting, the frequency of the alternations being 
usually about 100 periods per second, slitting the cores 
is insufficient to guard against eddy currents; nothing 
short of completely laminating the cores is a satisfac- 
tory remedy. I have here, thanks to the Brush Electric 
Engineering Company, an electromagnet of the special 
form that is used in the Brush arc lamp when required 
for the purpose of working in an alternating current 
circuit. It has two bobbins that are screwed up against 
the top of an iron box at the head of the lamp. The 
iron slab serves as a kind of yoke to carry the magnet- 
ism across the top. There are no fixed cores in the 
bobbins, which are entered by the ends of a pair of 
yoked plungers. Now in the ordinary Brush lamp for 
use with a steady current the plungers are simply two 
round pieces of iron tapped into a common yoke ; but 
for alternate current working this construction must 
not be used, and instead a U-shaped double -plunger is 
used, made up of laminated iron, riveted together. Of 
course it is no novelty to use a laminated core; that de- 
vice, first useJ. by Joule, and then by Cowper, has been 


repatented rather too often during the past 50 years to 
be considered as a recent invention. 

The alternate rapid reversals of the magnetism in the 
magnetic field of an electromagnet, when excited by 
alternating electric currents, sets up eddy currents in 
every piece of undivided metal within range. All 
frames, bobbin tubes, bobbin ends and the like must be 
most carefully slit, otherwise they will overheat. If a 
domestic flat-iron is placed on the top of the poles of a 
properly laminated electromagnet, supplied with alter- 
nating' currents, the flat-iron is speedily heated up by 
the eddy currents that are generated internally within 
it. The eddy currents set up by induction in neighbor- 
ing masses of metal, especially in good conducting 
metals, such as copper, give rise to many curious phe- 
nomena. For example, a copper disc or copper ring 
placed over the pole of a straight electromagnet so ex- 
cited is violently repelled. These remarkable phenom- 
ena have been recently investigated by Prof. Elihu 
Thomson, with whose beautiful and elaborate researches 
we have lately been made conversant in the pages of the 
technical journals. He rightly attributes many of the 
repulsion phenomena to the lag in phase of the alternat- 
ing currents thus induced in the conducting metal. The 
electromagnetic inertia, or self-inductive property of 
the electric circuit, causes the currents to rise and fall 
later in time than the electromotive forces by which 
they are occasioned. In all such cases the impedance 
which the circuit offers is made up of two things re- 
sistance and inductance. Both these causes tend to 
diminish the amount of current that flows, and the in- 
ductance also tends to delay the flow, 



I have already mentioned Hughes' researches on the 
form of electromagnet best adapted for rapid signaling. 
I have also incidentally mentioned the fact that where 
rapidly varying currents are employed, the strength of 
the electric current that a given battery can yield is de- 
termined not so much by the resistance of the electric 
circuit, but by its electric inertia. It is not a very easy 
task to explain precisely what happens to an electric 
circuit when the current is turned on suddenly. The 
current does not suddenly rise to its full value, being 
retarded by inertia. The ordinary law of Ohm in its 
simple form no longer applies; one needs to apply that 
other law which bears the name of the law of Helm- 
holtz, the use of which is to give us an expression, not 
for the final value of the current, but for its value at 
any short time, t, after the current has been turned on. 
The strength of the current after a lapse of a short time, 
t, cannot be calculated by the simple process of taking 
the electromotive force and dividing it by the resistance, 
as you would calculate steady currents. 

In symbols, Helmholtz's law is : 


- e L ) 

In this formula i t means the strength of the current 
after the lapse of a short time t; E is the electromotive 
force; R the resistance of the whole circuit; L its co- 
efficient of self-induction; arid e the number 2,7183, 



which is the base of the Napierian logarithms. Let us 
look at this formula; in its general form it resembles 
Ohm's law, but with a new factor, namely, the expres- 
sion contained within the brackets. This factor is nec- 
essarily a fractional quantity, for it consists of unity 
less a certain negative exponential, which we will pres- 
ently further consider. If the factor within brackets is 
a quantity less than unity, that signifies that i t will be 
less than E -j- R. Now the exponential of negative 
sign, and with negative fractional index, is rather a 
troublesome thing to deal with in a popular lecture. 
Our best way is to calculate some values, and then plot 
it out as a curve. When once you have got it into the 
form of a curve, you can begin to think about it, for 
the curve gives you a mental picture of the facts that 
the long formula expresses in the abstract. Accordingly 
we will take the following case: Let E = 10 volts; R = 
I ohm; and let us take a relatively large self-induction, 
so as to exaggerate the effect; say let L = 10 quads. 
This gives us the following: 




























In this case the value of the steady current as calcu- 



lated by Ohm's law is 10 amperes; but Helmholtz's 
law shows us that with the great self-induction, which 
we have assumed to be present, the current, even at the 
end of 30 seconds, has only risen up to within 95 per 
cent, of its final value; and only at the end of two min- 
utes has practically attained full strength. These values 
are set out in the highest curve in Fig. 54, in which, 
however, the further supposition is made that the num- 
ber of spirals S in the coils of the electromagnet is 100, 
so that when the current attains its full value of 10 

10 20 40 60 80 100 120 


amperes the full magnetizing power will be Si = 
1,000. It will be noticed that the curve rises from zero 
at first steeply and nearly in a straight line, then bends 
over, and then becomes nearly straight again as it grad- 
ually rises to its limiting value. The first part of the 
curve that relating to the strength of the current after 
a very small interval of time is the period within 
which the strength of the current is governed by inertia 
(i. e., the self-induction) rather than by resistance. In 
reality the current is not governed either by the self- 
induction or by the resistance alone, but by the ratio of 
the two. This ratio is sometimes called the " time-con- 


stant " of the circuit, for it represents the time which 
the current takes in that circuit to rise to a definite 

fraction of its final value. This definite fraction is the 


fraction ; or in decimals, 0.634. All curves of rise 

of current are alike in general shape they differ only 
in scale; that is to say, they differ only in the height to 
which they will ultimately rise, and in the time they 
will take to attain this fraction of their final value. 

Example (1). Suppose E = 10; R = 400 ohms; L = S. 
The final value of the current will be 0.025 ampere or 25 
milliamperes. Then the time-constant will be 8 * 400 = 
l-50th second. 

Example (2). The P. O. Standard "A" relay has R = 400 
ohms; L 3.25. It works with 0.5 milliampere current, and 
therefore will work with 5 Daniell cells through a line of 
9,600 ohms. Under these circumstances the time-constant 
of the instrument on short circuit is 0.0081 second. 

It will be noted that the time-constant of a circuit can 
be reduced either by diminishing the self-induction, or 
by increasing the resistance. In Fig. 54 the position of 
the time-constant for the top curve is shown by the 
vertical dotted line at 10 seconds. The current will 
take 10 seconds to rise to 0.634 of its final value. This 
retardation of the rise of current is simply due to the 
presence of coils and electromagnets in the circuit; the 
current as it grows being retarded because it has to 
create magnetic fields in these coils, and so sets up op- 
posing electromotive forces that prevent it from grow- 
ing all at once to its full strength. Many electricians 
unacquainted with Helmholtz's law have been in the 


habit of accounting for this by saying that there is a 
lag in the iron of the electromagnet cores. They tell 
you that an iron core cannot be magnetized suddenly; 
that it takes time to acquire its magnetism. They think 
it is one of the properties of iron. But we know that 
the only true time-lag in the magnetization of iron 
that which is properly termed "viscous hysteresis" 
does not amount to three per cent, of the whole amount 
of magnetization, takes comparatively a long time to 
show itself, and cannot therefore be the cause of the 
retardation which we are considering. There are also 
electricians who will tell you that when magnetization 
is suddenly evoked in an iron bar there are induction 
currents set up in the iron which oppose and delay its 
magnetization. That they oppose the magnetization is 
perfectly true; but if you carefully laminate the iron 
so as to eliminate eddy currents, you will find, strangely 
enough, that the magnetism rises still more slowly to 
its final value. For by laminating the iron you have 
virtually increased the self-inductive action, and in- 
creased the time-constant of the circuit, so that the 
currents rise more slowly than before. The lag is not 
in the iron, but in the magnetizing current, and the 
current being retarded, the magnetization is, of course, 
retarded also. 


Now let us apply these most important though rather 
intricate considerations to the practical problems of 
the quick working of the electromagnet. Take the case 
of an electromagnet forming some part of the receiving 


apparatus of a telegraph system, in which it is desired 
to secure very rapid working. Suppose the two coils 
that are wound upon the horseshoe core are connected 
together in series. The coefficient of self-induction for 
these two is four times as great as that of either sepa- 
rately; coefficients of self-induction being proportional 
to the square of the number of turns of wire that sur- 
round a given core. Now if the two coils, instead of 
being put in series, are put in parallel, the coefficient 
of self-induction will be reduced to the same value as if 
there were only one coil, because half the line current 
(which is practically unaltered) will go through each 
coil. Hence the time-constant of the circuit when the 
coils are in parallel will be a quarter of that which it is 
when the coils are in series; on the other hand, for a 
given line current, the final magnetizing power of the 
two coils in parallel is only half what it would be with 
the coils in series. The two lower curves in Fig. 54 illus- 
trate this, from which it is at once plain that the mag- 
netizing power for very brief currents is greater when 
the two coils are put in parallel with one another than 
when they are joined in series. 

Now this circumstance has been known for some time 
to telegraph engineers. It has been patented several 
times over. It has formed the theme of scientific papers 
which have been read both in France and in England. 
The explanation generally given of the advantage of 
uniting the coils in parallel is, I think, fallacious; 
namely, that the "extra currents" (i. e., currents due to 
self-induction) set up in the two coils are induced in 
such directions as tend to help one another when the 


coils are in series, and to neutralize one another when 
they are in parallel. It is a fallacy, because in neither 
case do they neutralize one another. Whichever way 
the current flows to make the magnetism, it is opposed 
in the coils while the current is falling by the so-called 
extra currents. If the current is rising in both coils at 
the same moment, then, whether the coils are in series 
or in parallel, the effect of self-induction is to retard 
the rise of the current. The advantage of parallel 
grouping is simply that it reduces the time-constant. 


One may consider the question of grouping the bat- 
tery cells from the same point of view. How does the 
need for rapid working and the question of time-con- 
stant affect the best mode of grouping the battery cells ? 
The amateur's rule, which tells you to so arrange your 
battery that its internal resistance should be equal to 
the external resistance, gives you a result wholly wrong 
for rapid working. The supposed best arrangement 
will not give you (at the expense even of economy) the 
best result that might be got out of the given number 
of cells. Let us take an example and calculate it out, 
and place the results graphically before our eyes in the 
form of curves. Suppose the line and electromagnet 
have together a resistance of six ohms, and that we have 
24 small DanielFs cells, each of electromotive force, say, 
one volt, and of internal resistance four ohms. Also 
let the coefficient of self-induction of the electromagnet 
and circuit be six quadrants. When all the cells are in 
series, the resistance of the battery will be 96 ohms, the 


total resistance of the circuit 102 ohms, and the full 
value of the current 0.235 ampere. When all the cells 
are in parallel the resistance of the battery will be 0.133 
ohm, the total resistance 6.133 ohms, and the full value 
of the current 0.162 ampere. According to the amateur 
rule of grouping cells so that internal resistance equals 
external, we must arrange the cells in four parallels, 
each having six cells in series, so that the internal re- 
sistance of the battery will be six ohms, total resistance 
of circuit 12 ohms, full value of current 0.5 ampere. 


Now the corresponding time-constants of the circuit in 
the three cases (calculated by dividing the coefficient of 
self-induction by the total resistance) will be respect- 
ively in series, 0.06 sec.; in parallel, 0.96 sec.; grouped 
for maximum steady current, 0.5 sec. From these data 
we may now draw the three curves, as in Fig. 55, wherein 
the abscissae are the values of time in seconds, and the 
ordinates the current. The faint vertical dotted lines 
mark the time-constants in the three cases. It will be 
seen that when rapid working is required the magnetiz- 
ing current will rise, during short intervals of time, 


more rapidly if all the cells are put in series than it will 
do if the cells are grouped according to the amateur 

When they are all put in series, so that the battery 
has a much greater resistance than the rest of the cir- 
cuit, the current rises much more rapidly, because of the 
smallness of the time-constant, although it never attains 
the same ultimate maximum as when grouped in the 
other way. That is to say, if there is self-induction as 
well as resistance in the circuit, the amateur rule does 
not tell you the best way of arranging the battery. 
There is another mode of regarding the matter which 
is helpful. Self-induction, while the current is grow- 
ing, acts as if there were a sort of spurious addition to 
the resistance of the circuit; and while the current is 
dying away it acts of course in the other way, as if there 
were a subtraction from the resistance. Therefore you 
ought to arrange the batteries so that the internal resist- 
ance is equal to the real resistance of the circuit, plus 
the spurious resistance during that time. But how 
much is the spurious resistance during that time? It 
is a resistance proportional to the time that has elapsed 
since the current was turned on. So then it comes to 
the question of the length of time for which you want 
to work it. What fraction of a. second do you require 
your signal to be given in ? What is the rate of the 
vibrator of your electric bell ? Suppose you have settled 
that point, and that the short time during which the 
current is required to rise is called t; then the apparent 
resistance at time t after the current is turned on is 
given by the formula: 



R t = R x e L - 


I may here refer to some determinations made by M. 
Vaschy, 4 respecting the coefficients of self-induction of 
the electromagnets of a number of pieces of telegraphic 
apparatus. Of these I must only quote one result, which 
is very significant; it relates to the electromagnet of a 
Morse receiver of the pattern habitually used on the 
French telegraph lines. 

Z,, in quadrants. 

Bobbins, separately, without iron cores 0.233 and 0.265 

Bobbins, separately, with iron cores 1.65 and 1.71 

Bobbins, with cores joined by yoke, coils in series 6.37 

Bobbins, with armature resting on poles 10.68 

It is interesting to note how the perfecting of the 
magnetic circuit increases the self-induction. 

Thanks to the kindness of Mr. Preece, I have been 
furnished with some most valuable information about 
the coefficients of self-induction, and the resistance of 
the standard pattern of relays and other instruments 
which are used in the British postal telegraph service, 
from which data one is able to say exactly what the 
time-constants of those instruments will be on a given 
circuit, and how long in their case the current will take 
to rise to any given fraction of its final value. Here let 
me refer to a very capital paper by Mr. Preece in an old 
number of the "Journal of the Society of Telegraph 
Engineers," a paper ff On Shunts," in which he treats 
this question, not as perfectly as it could now be treated 

4 " Bulletin de la SocietS Internationale des Electriciens," 1886. 


with the fuller knowledge we have in 1890 about the 
coefficients of self-induction, but in a very useful and 
practical way. He showed most completely that the 
more perfect the magnetic circuit is though, of course, 
you are getting more magnetism from your current 
the more is that current retarded. Mr. Preece's mode 
of experiment was extremely simple; he observed the 
throw of the galvanometer, when the circuit which con- 
tained the battery and the electromagnet was opened by 
a key which at the same moment connected the electro- 


502 26 


magnet wires to the galvanometer. The throw of the 
galvanometer was assumed to represent the extra cur- 
rent which flowed out. Fig. 56 represents a few of the 
results of Mr. Preece's paper. Take from an ordinary 
relay a coil, with its iron core, half the electromagnet, 
so to speak, without any yoke or armature. Connect it 
up as described, and observe the throw given to the 
galvanometer. The amount of throw obtained from the 
single coil was taken as unity, and all others were com- 
pared with it. If you join up two such coils as they 
are usually joined, in series, but without any iron yoke 
across the cores, the throw was 17. Putting the iron 


yoke across the cores, to constitute a horseshoe form, 
496 was the throw; that is to say, the tendency of this 
electromagnet to retard the current was 496 times as 
great as that of the simple coil. But when an armature 
was put over the top the effect ran up to 2,238. By 
the mere device of putting the coils in parallel, instead 
of in series, the 2,238 came down to 502, a little less 
than the quarter value which would have been expected. 
Lastly, when the armature and yoke were both of them 
split in the middle, as is done in fact in all the standard 
patterns of the British Postal Telegraph relays, the 
throw of the galvanometer was brought down from 502 
to 26. Eelays so constructed will work excessively rap- 
idly. Mr. Preece states that with the old pattern of 
relay having so much self-induction as to give a galva- 
nometer throw of 1,688, the speed of signaling was only 
from 50 to 60 words per minute; whereas with the 
standard relays constructed on the new plan, the speed 
of signaling is from 400 to 450 words per minute. It 
is a very interesting and beautiful result to arrive at 
from the experimental study of these magnetic circuits. 


In considering the forms that are best for rapid ac- 
tion, it ought to be mentioned that the effects of hys- 
teresis in retarding changes in the magnetization of 
iron cores are much more noticeable in the case of 
nearly closed magnetic circuits than in short pieces. 
Electromagnets with iron armatures in contact across 
their poles will retain, after the current has been cut 
off, a very large part of their magnetism, even if the 


cores be of the softest of iron. But so soon as the arma- 
ture is wrenched off the magnetism disappears. An air- 
gap in a magnetic circuit always tends to hasten de- 
magnetizing. A magnetic circuit composed of a long 
air path and a short iron path demagnetizes itself much 
more rapidly than one composed of a short air path and 
a long iron path. In long pieces of iron the mutual 
actions of the various parts tend to keep in them any 
magnetization that they may possess; hence they are 
less readily demagnetized. In short pieces where these 
mutual actions are feeble, or almost absent, the mag- 
netization is less stable and disappears almost instantly 
on the cessation of the magnetizing force. Short bits 
and small spheres of iron have no "magnetic memory/' 
Hence the cause of the commonly received opinion 
among telegraph engineers that for rapid work electro- 
magnets must have short cores. As we have seen, the 
only reason for employing long cores is to afford the 
requisite length for winding the wire which is neces- 
sary for carrying the needful circulation of current to 
force the magnetism across the air-gaps. If, for the 
sake of rapidity of action, length has to be sacrificed, 
then the coils must be heaped up more thickly on the 
short core's. The electromagnets in American patterns 
of telegraphic apparatus usually have shorter cores and 
a relatively greater thickness of winding upon them 
than those of European patterns. 




THE task before me to-night comprises the following 
matters: First, to speak of that particular variety of 
the electromagnet in which the iron core, instead of 
being attached to the coils, is movable, and is attracted 
into them. Secondly, to speak of the modes of equaliz- 
ing the pull of electromagnets of various sorts over their 
range of action. Thirdly, to describe sundry mechan- 
isms which depend on electromagnets. Lastly, to dis- 
cuss the modes of prevention or diminution of the spark- 
ing which is so almost invariably found to accompany 
the break of circuit when one is using an electromagnet. 


First, then, let me deal with the apparatus wherein 
an iron core is attracted into a tubular coil or solenoid, 
an apparatus which, for the sake of brevity, I take the 
liberty of naming as the coil-and-plunger. Now, from 
quite early times, from 1822 at any rate, it was known 
that a coil would attract a piece of iron into it, and that 
this action resembled somewhat the action of a piston 
going into a cylinder resembled it, I mean to say, in 
possessing an extended range of action. The use of 
such a device as the coil-and-plunger was even patented 


in this country in 1846 under the name of " a new elec- 
tromagnet." Electromagnetic engines, or motors, were 
made on this plan by Page, and afterward by others, 
and it became generally known as a distinct device. 
But even now, if you inquire into the literature of the 
text-books to know what are the peculiar properties of 
the coil-and-plunger arrangement, you will find that the 
books give you next to no information. They are con- 
tent to deal with the thing in very general terms by 
saying: Here is a sort of sucking magnet; the core is 
attracted in. Some books go so far as to tell you that 
the pull is greatest when the core is about half way in ; 
a statement which is true in one particular case, but 
false in a great many others. Another book tells you 
that the pull is greatest at a point one centimetre below 
the centre of the coil, for plungers of all different lengths 
which is quite untrue. Another book tells you that 
a wide coil pulls less powerfully than a narrow one; a 
statement which is true for some cases and not for 
others. The books also give you some approximate 
rules, which, however, are very little to the point. The 
reason why this ought to receive much more careful 
consideration is because in this mechanism of coil-and- 
plunger we have a real means not only of equalizing, 
but also of vastly extending the range of the pull of the 
electromagnet. Let us take a very simple example for 
the sake of contrasting the range of action of the ordi- 
nary electromagnet with the range of action of the coil- 

Here are some numbers which are given in a paper 
with which I have long been familiar, a paper read by 



the late Mr. Eobert Hunt in 1856, before the Institution 
of Civil Engineers, with that eminent engineer, Eobert 
Stephenson, in the chair. Mr. Hunt described the vari- 
ous types of motors, and spoke of this question of the 
range of action. He recounted some experiments of 
his own in which the following was the range of action. 

There was a horseshoe elec- 
tromagnet which at distance 
zero that is, when its arma- 
ture was in contact pulled 
with a pull of 220 pounds; 
when the distance was made 
only y-oVoth of an inch (4 
mils), the pull fell to 90 
pounds; and when the dis- 
tance was increased to 20 
mils, T V tn f an inch)? the 
pull fell to only 36 pounds. 
The difference from 220 to 
36 was within a range of 
g^th of an inch. He con- 
trasts this with the results 
given by another mechanism, not quite the simple coil- 
and-plunger, but a variety of electromagnet brought out 
about the year 1845 by a Dane, living in Liverpool, 
named Hjorth, wherein a sort of hollow, truncated cone 
of iron (Fig. 57), with coils wound upon it a hollow 
electromagnet, in fact was caused to act on another 
electromagnet, one being caused to plunge into the 
other. Now we have no information what the pull was 
at distance zero with this curious arrangement of 



Hjorth's, bat at a distance of one inch the pull (with 
a very much larger apparatus than Hunt's) was 160 
pounds, the pull at three inches was 88 pounds, at five 
inches 72 pounds. Here, then, we have a range of action 
going not over g^th of an inch, but over five inches, and 
falling not from 220 to 36, but from 160 to 72, obviously 
a much more equable kind of range. At the Institution 
of Civil Engineers on that occasion a number of the 
most celebrated men, Joule, Cowper, Sir William Thom- 
son, Mr. Justice Grove, and Prof. Tyndall, discussed 
these matters discussed them up and down from the 
point of view of range of action, and from the point of 
view of the fact that there was no means of working 
them at that time except by the consumption of zinc in 
a primary battery; and they all came to the conclusion 
that electric motors would never pay. Robert Stephen- 
son summed up the debate at the end in the following 
words: "In closing the discussion," he remarked, 
"there could be no doubt from what had been said that 
the application of voltaic electricity, in whatever shape it 
might be developed, was entirely out of the question 
commercially speaking. Without, however, considering 
the subject in that point of view, the mechanical appli- 
cations seemed to involve almost insuperable difficulties. 
The power exhibited by electromagnetism, though very 
great, extended through so small a space as to be prac- 
tically useless. A powerful magnet might be compared., 
for the sake of illustration, to a steam engine with an 
enormous piston but with an exceedingly short stroke ; 
such an arrangement was well known to be very undesir- 


Well, from the discussion in 1856 when this ques- 
tion of the length of range was so distinctly set forth 
down to the present, there have been a large number of 
attempts to ascertain exactly how to design a long range 
electromagnet, and those who have succeeded have, as a 
general rule, not been the theorists; rather they have 
been men compelled by force of circumstances to arrive 
at their result by some kind of shall we call it " de- 
signing eye," by having a sort of intuitive perception of 
what was wanted, and going about it in some rough- 
and-ready way of their own. Indeed, I am afraid had 
they tried to get much light from calculations based on 
orthodox notions respecting the surface distribution 
of magnetism, and all that kind of thing, they would 
not have been much helped. There is our old friend, 
the law of inverse squares, which would of course turn 
up the first thing, and they would be told that it would 
be impossible to have a magnet that pulled equally 
through any range, because the pull was certain to vary 
inversely according to the square of the distance. I 
noticed that, in a report of my second lecture in one of 
the London journals, I am announced to have said that 
the law of inverse squares did not apply to electric- 
forces. I beg to remark I have said no such thing. It 
is well to be precise as to what one does say. There 
has been a lively discussion going on quite lately whether 
sound varies as the square of the distance or rather, 
whether the intensity of it does and the people who 
dispute on both sides of the case do not seem to know 
what the law of inverse squares means. I have also seen 
the statement made last week in the columns of The 


Times, by one who is supposed to be an eminent author- 
ity on eyesight, that the intensity of the color of a scar- 
let geranium varies inversely with the square of the dis- 
tance from which you s6e it. More utter nonsense was 
never written. The fact is, the law of inverse squares, 
which is a perfectly true mathematical law, is true not 
only for electricity, but for light, for sound, and for 
everything else, provided it is applied to the one case to 
which a law of inverse squares is applicable. That law 
is a law expressing the way in which action at a distance 
falls off when the thing from which the action is pro- 
ceeding is so small compared with the distance in ques- 
tion that it may be regarded as a point. The law of 
inverse squares is the law universal of action proceeding 
from a point. The music of an orchestra at 10 feet 
distance is not four times as loud as at 20 feet distance; 
for the size of an orchestra cannot be regarded as a 
mere point in comparison with these distances. If you 
can conceive of an object giving out a sound, and the 
object being so small in relation to the distance at which 
you are away from it that it is a point, the law of in- 
verse squares is all right for that, not for the intensity 
of your hearing, but for the intensity of that to which 
your sensation is directed. In no case, however, are 
sensations absolutely proportional to their causes. When 
the magnetic action proceeds from something so small 
that it may be regarded as a point compared with the 
distance, then the law of inverse squares is necessarily 
and mathematically true. 

You may remember that I produced an apparatus 
(Fig. 27) which I said was. the only apparatus hitherto 


devised which did directly prove, experimentally, the 
law of inverse squares for the case of a magnetic pole. 
There was in it a pole, virtually a point at a considera- 
ble distance from a small magnetic needle, which was 
also virtually a point. 

The law of inverse squares is true ; but it is not what 
one works with when one deals with electromagnets 
having ends of a visible size, acting on armatures them- 
selves of visible sizes, and quite close to them. If you 
take a case which never occurs in practice, an armature 
of hard steel, permanently magnetized, so far away from 
an electromagnet (or rather from one pole only) that 
the distance between the one pole and the armature on 
which you are acting is so very great compared with 
each of them that each of them may be regarded by 
comparison as a point, then the law of inverse squares 
may be rightly applied, but not unless. 

Now we want to arrive at a true law. We want to 
know exactly what the law of action of the coil-and- 
plunger is. It is not a very difficult thing to work out, 
provided you get hold of the right ideas. We must 
begin with a simple case, that of a short coil consisting 
of but one turn, acting on a single point pole. From 
this we may proceed to consider the effect on a point 
pole of a long tube of coil. Then we may go on to a 
more complex case of the tube coil acting on a very long 
iron core; and last of all from the very long iron core 
we may pass to the case of a short core. 

You all know how a long tube of coil such as this 
will act on an iron core. Let us make an experiment 
with it, I turn on the current so that it circulates 


around the coil along the tube, and when I hold in front 
of the aperture of the tube this rod of soft iron, it is 
sucked into the coil. When I pull it out a little way 
it runs back, as with a spring. The current happens to 
be a strong one 'about 25 amperes; there are about 700 
turns of wire on the coil. The rod is about one inch in 
diameter and 20 inches long. So great is the pull that 
I cannot pull it entirely out. The pull was very small 
when the rod was outside, but as soon as it gets in it is 
pulled actively, runs in and settles down with the ends 
equally protruding. The tubular coil I have been using 
is about 14 inches long; but now let us consider a 
shorter coil. Here is one only half an inch from one 
end to the other, but I have one somewhere still shorter, 
so short that the length, parallel to the axis, is very 
small compared with the diameter of the aperture with- 
in. The wire on it consists of but one single turn. 
Taking such a coil, treating it as only one single ring, 
with the current going once round, in what way does it 
act on a magnet that is placed on the axis ? First of 
all, take the case of a very long permanently magnet- 
ized steel magnet, so long, indeed, that any action on 
the more distant pole is so feeble that it may be disre- 
garded altogether and only one pole, say the north pole, 
is near the coil. In what way will that single turn of 
coil act on that single pole ? This is the rule, that the 
pull does not vary inversely as the square of the dis- 
tance, nor as any power at all of the distance measured 
straight along the axis, but inversely as the cube of the 
slant distance. Let the point in Fig. 58 represent 
the centre of the ring, its radius being y. The line OP 


is the axis of the ring, and the distance from to P 
we will call x. The slant distance from P to the ring 
we call a. Then the pull on the axis toward the centre 
of this coil varies inversely as the 
cube of a. That law can be plotted 
out in a curve for the sake of ob- 
serving the variations of pull at 
various points along the axis. Al- 
low me to draw your attention to 
FIG. 58. ACTION OF SINGLE Fig. 59, which represents a section 

COIL ON POINT POLE ON Qr ed y j ew of the coil> At yari _ 

ous distances right and left of the 
coil are plotted out vertically the corresponding force, 
the calculations being made for a current of 10 amperes, 
circulating once around a ring of one centimetre radius. 
The force with which such a current acts on a magnetic 
pole of unit strength placed at the central point is 6.28 
dynes. If the pole is moved away down the axis, the 
pull is diminished; at a distance away equal in length to 

O.M7 0;1S 0.13 

4 6 a 


the radius it has fallen to 2.22 dynes. At a distance 
equal to twice the radius, or one diameter, it is only 0.56 
dyne, less than one-tenth of what it was at the centre. 
At two diameters it has fallen to 0.17 dyne, or less than 
three per cent.; and the force at three diameters is only 
about two per cent, of that at the centre. 


If, then, we could take a very long magnet, we may 
utterly neglect the action on the distant pole. If I had 
a long steel magnet with the south pole five or six feet 
away, and the north pole at a point three diameters 
(i. e., six centimetres in this case) distant from the mouth 
of the coil, then the pull of the current in one spiral on 
the north pole three diameters away would be practi- 
cally negligible; it would be less than two per cent, of 
what the pull would be of that single coil when the pole 
was pushed right up into it. But now, in the case of 
the tubular coil, consisting of at least a whole layer of 
turns of wire, the action of all of the turns has to be 
considered. If the nearest of the turns of wire is at a dis- 
tance equal to three diameters, all the other turns of 
wire will be at greater distances, and, therefore, if we 
may neglect such small quantities as two per cent, of 
the whole amount, we may neglect their action also; for 
it will be still smaller in amount. Now, for the pur- 
pose of arriving at the action of a whole tube of coil, I 
will adopt a method of plotting devised by Mr. Sayers. 
Suppose we had a whole tube coiled with copper wire 
from end to end, its action would be practically the 
same as though the copper wire were gathered together 
in small numbers at distant intervals? If, for example, 
I count the number of turns in a centimetre length of 
the actual tubular coil, which I used in my first experi- 
ment, I find there are four. Now if, instead of having 
four wires distributed over the centimetre, I had one 
stout wire in the middle of that space to carry four 
times the current, the general effect would be the same. 
This diagram (Fig. 60) is calculated out on the sup- 



position that the effect will be not greatly different if 
the wires were aggregated in that way, and it is easier 
to calculate. If, beginning at the end of the tube 
marked A, we take the wires over the first centimetre of 
length and aggregate them, we can draw a curve, 
marked 1, for the effect of that lot of wires. For the 
next lot we could draw a similar curve, but instead of 
drawing it on the horizontal line we will add the several 
heights of the second curve on to those of the first, and 
that gives the curve marked 2; for the third part add 
the ordinates of another similar curve, and so gradually 



build up a final curve for the total action of this tubu- 
lar coil on a unit pole at different points along the axis. 
This resultant curve begins about 2^ diameters away 
from the end, rises gently, and then suddenly, and then 
turns over and becomes nearly flat with a long level It does not rise any more after a point about 2^ 
diameters along from A; the curve at that point be- 
comes practically flat, or does not vary more than about 
one per cent., however long the tube may be. For ex- 
ample, in a tubular coil one inch in diameter and 20 
inches long, there will be a uniform magnetic field for 
about 15 inches along the middle of the coil. In a 


tubular coil three centimetres in diameter and 40 
centimetres long, there will "be a uniform magnetic field 
for about 32 centimetres along the middle of the coil. 
The meaning of this is that the value of the magnetic 
forces down the axis of that coil begins outside the 
mouth of the tube, increases, rises to a certain maxi- 
mum amount a little within the mouth of the tube, and 
after that is perfectly constant nearly all the way along 
the tube, and then falls off symmetrically as you get to 
the other end. The ordinates drawn to the curve rep- 
resent the forces at corresponding points along the axis 
of the tube, and may be taken to represent not simply 
the magnetizing force, but the pull on a magnetic pole 
at the end of an indefinitely long, thin steel magnet of 
fixed strength. 

The rule for calculating the intensity of the magnetic 
force at any point on the axis of the long tubular coil with- 
in this region where the force is uniform is : H = ^ X the 

ampere turns per centimetre of length. And, as the 
total magnetizing power of a tubular coil is proportional 
not only to the intensity of the magnetic force at any point, 
but also to the length, the integral magnetizing effect on a 
piece of iron that is inserted into the coil may be taken as 

practically equal to TT X the total number of ampere turns 

in that portion of the tubular coil which surrounds the 
iron. If the iron protrudes as much as three diameters at 

both ends, the total magnetizing force is simply TT X the 
whole number of ampere turns. 

Now that case is of course not the one we are usually 


dealing with. We cannot procure steel magnets with 
unalterable poles of fixed strength. Even the hardest 
steel magnet, magnetized so as to give us a permanent 
pole near or at the end of it quite close up to the end 
of it when you put it into a magnetizing coil becomes 
by that fact further magnetized. Its pole becomes 
strengthened as it is drawn in, so that the case of an 
unalterable pole is not one which can actually be real- 
ized. One does not usually work with steel; one works 
with soft iron plungers which are not magnetized at all 
when at a distance away, but become magnetized in the 
act of being placed at the mouth of the coil, and which 
become more highly magnetized the further they go in. 
They tend, indeed, to settle down, with the ends pro- 
truding equally, for that is the position where they most 
nearly complete the magnetic circuit; where, therefore, 
they are most completely and highly magnetized. Ac- 
cordingly we have this fact to deal with, .and whatever 
may be the magnetizing forces all along the tube, the 
magnetism of the entering core will increase as it goes 
on. We must therefore have recourse to the following 
procedure: We will construct a curve in which we will 
plot not simply the magnetizing forces of the spiral at 
different points, but the product of the magnetizing 
forces into the magnetism of the core which itself in- 
creases as the core moves in. The curve with a flat top 
to it corresponds to an ideal case of a single pole of 
constant strength. We wish to. pass from this to a curve 
which shall represent a real case, with an iron core. 
Let us still suppose that we are using a very long core, 
one so long that when the front pole has entered the 


coil the other end is still a long way off. With an iron 
core of course it depends on the size and quality of the 
iron as to how much magnetism you get for a given 
amount of magnetizing power. When the core has en- 
tered up to a certain point you have all the magnetizing 
forces up to that point acting on it; it acquires a cer- 
tain amount of magnetism, so that the pull will neces- 
sarily go on increasing and increasing, although the in- 
tensity of the magnetic force from point to point along 



the axis of the coil remains the same, until within 
about two diameters from the far end. Although the 
magnetic force inside the long spiral remains the same, 
because the magnetism of the core is increasing, the 
pull goes on increasing and increasing (if the iron does 
not get saturated) at an almost uniform rate all the 
way up until the piece of iron has been poked pretty 
nearly through to the distant end. In Fig. 61 a tubu- 
lar coil, B A, is represented. Suppose a long iron core 
is placed on the axis to the right, and that its end is 


gradually brought up toward B. When it arrives at X 
the pnll becomes sensible, and increases at first rapidly, 
as the core enters the mouth of the tube, then gently, 
as the core travels along, attaining a maximum, C, 
about at the further end, A, of the tube. When it ap- 
proaches to the other end, A, it comes to the region 
where the magnetizing force falls off, but the magnetism 
is still going on increasing, because something is still 
being added to the total magnetizing power, and these 
two effects nearly balance one another, so that the pull 
arrives at the maximum. This is the highest point, (7, 
on the curve ; the greatest pull occurring just as the end 
of the iron core arrives at the bottom or far end of the 
tubular coil ; from which point there is a very rapid 
falling off. The question of rapidity of descent from 
that point depends only on how long the core is. If 
the core is a very long one, so that its other pole is still 
very far away, you have a long, slow descent going on 
over some three diameters, and gradually vanishing. 
If, however, the other pole is coming up within measur- 
able distance of B, then the curve will come down more 
rapidly to a definite point, X\. To take a simple case 
where the iron core is twice as long as the coil, its curve 
will descend in pretty nearly a straight line down to a 
point such that the ends of the iron rod stand out 
equally from the ends of the tube. 

Precisely similar effects will occur in all other cases 
where the plunger is considerably longer than (at least 
twice as long as) the coil surrounding it. If you take a 
different case, however, you will get another effect. 
Take the case of a plunger of the same length as the 


coil, then this is what necessarily happens. At first the 
effects are much the same; but as soon as the core has 
entered about half, or a little more than half, its length 
you begin to have the action of the other pole that is 
left protruding outside tending to pull the plunger 
back ; and although the magnetizing force goes on in- 
creasing the further the plunger enters, the repulsion 
exerted by the coil on the other pole of the plunger 
keeps increasing still faster as this end nears the mouth 
of the coil. In that case the maximum will occur at a 
point a little further than half way along the coil, and 
from that point the curve will descend and go to zero 
at A; that is to say, there will be no pull when both 
ends of the plunger coincide with the two ends of the 
coil. If you take a plunger that is a little shorter than 
the coil, then you find that the attraction comes down 
to zero at an earlier period still. The maximum pull 
occurs earlier, and so does the reduction of the pull to 
zero; there being no action at all upon the short core 
when it lies wholly within that region of the tube within 
which the intensity of the magnetic force is uniform. 
That is to say, for any portion of this tube correspond- 
ing to the flat top of the curve of Fig. 60, if the plunger 
of iron is so short as to lie wholly within that region, 
then there is no action upon it; it is not pulled either 
way. Now these things can be not only predicted by 
the help of such a law as that, but verified by experi- 
ment. Here is a set of tubular coils which we use at 
the Finsbury Technical College for the purpose of veri- 
fying these laws. There is one here about nine inches 
long, one about half that length, another just a quarter, 


They are all made alike in this way, that they have ex- 
actly the same weight of copper wire, cut from the same 
hank, upon them. There are, of course, more turns on 
the long one than on the shorter, because with the 
shorter ones each turn requires, on the average, a larger 
amount of wire, and therefore the same weight of wire 
will not make the same number of windings. We use 
that very simple apparatus, a Salter's balance, to meas- 
ure the pull exerted down to different distances on 
cores of various lengths. You find in every case the 
pull increases and becomes a maximum, then dimin- 
ishes. We will now make the experiment, taking first 
a long plunger, roughly about twice as long as the coil. 
The pull increases as the plunger goes down, and the 
maximum pull occurs just when the lower end gets to 
the bottom ; beyond that the pull is less. Using the 
same plunger with these shorter coils, one finds the 
same thing, in fact more marked, for we have now a 
core which is more than twice the length of the coil. 
So we find, taking in all these cases, that the maximum 
pull occurs not when the plunger is half way in, as the 
books say, but when the bottom end of it is just begin- 
ning to come out through the bottom of the coil that 
we are using. If, however, we take a shorter plunger, 
the result is different. Here is one just the same length 
as the coil. With this one the maximum pull does occur 
when the core is about half way in; the maximum pull 
is just about at the middle. Again, with a very short 
core here is one about one-sixth of the length of the 
coil the maximum pull occurs as it is going into the 
mouth of the coil; and when both ends have gone in so 


far that it gets into the region of equable magnetic field 
there is no more pull on one end than on the other; one 
end is trying to move with a certain force down the 
tube, arid the other end is trying to move with exactly 
equal force up the tube, and the two balance one an- 
other. If we carry that to a still more extreme case, 
and employ a little round ball of iron to explore down 
the tube, you will find this curious result, that the only 
place where any pull occurs on the ball is just as it 
is going in at the mouth. For about half an inch in 
the neck of the coil there is a pull; but there is no pull 
down the interior of the tube at all, and there is no 
measurable pull outside. 

Now these actions of the coil on the core are capable 
of being viewed from another standpoint. Every en- 
gineer knows that the work done by a force has to be 
measured by multiplying together the force and the 
distance through which its point of application moves 
forward. Here we have a varying force acting over a 
certain range. We ought, therefore, to take the amount 
of the force at each point, and multiply that by the ad- 
jacent little bit of range, averaging the force over that 
range, and then take the next value of force with the 
next little bit of range, and so consider in small portions 
the work done along the whole length of travel. If we 
call the length of travel x the element of length must 
be called dx. Multiply that by/, the force. The force 
multiplied by the element of length gives us the work, 
dw, done in that short range. Now the whole work 
over the whole travel is made up of the sum of such 
elements all added together; that is to say, we have to 


take all the various values of/, multiply each by its own 
short range dx, and the sum of all those, writing/ for 

the sum, would be equal to the sum of all the work; 
that is to say, the whole work done in putting the thing 
together will be written : 

w =jfdx. 

Now what I want you to think about is this: Here, 
say, is a coil, and there is a distant core. Though there 
is a current in the coil, it is so far away from the core 
that practically there is no action : bring them nearer 
and nearer together; presently they begin to act on one 
another; there is a pull, which increases as the core en- 
ters, then comes to a maximum, then dies away as the 
end of the core begins to protrude at the other side. 
There is no further pull at all when the two ends stand 
out equally. Now there has been a certain total 
amount of work done by this apparatus. Every engineer 
knows that if we can ascertain the force at every point 
along the line of travel the work done in that travel is 
readily expressed by the area of the force curve. Think 
of the curve X C X\, in Fig. 61, the ordinates of which 
represent the forces. The whole area underneath this 
curve represents the work done by the system, and 
therefore represents equally the work you would have 
to do upon it in pulling the system apart. The area 
under the curve represents the total work done in at- 
tracting in the iron plunger, with a pull distributed over 
the range X X\. 

Now I want you to compare that with the case of an 


electromagnet where, instead of having this distributed 
pull, you have a much stronger pull over a much shorter 
range. I have endeavored to contrast the two in the 
other curves drawn in Fig. 61. Suppose we have our 
coil, and suppose the core, instead of being made of one 
rod such as this, were made in two parts, so that they 
could be put together with a screw in the middle, or 
fastened together in any other mechanical way. Now 
first treat this rod as a single plunger, screw the two 
parts together, and begin with the operation of allow- 
ing it to enter into the coil ; the work done will be the 
area under the curve which we have already considered. 
Let us divide the iron core into two. First of all put 
in one end of it ; it will be attracted up in a precisely 
similar fashion, only, being a shorter bar, the maximum 
would be a little displaced. Let it be drawn in up to 
half way only.; we have now a tube half filled with iron, 
and in doing so we shall have had a certain amount of 
work done by the apparatus. As the piece of iron is 
shorter, the force curve, which ascends from ^to Y\ 9 
will lie a little lower than the curve XC X\ ; but the 
area under that lower curve, which stops half way, will 
be the work done by the attraction of this half core. 
Now go to the other end and put in the other half of 
the iron You now have not only the attraction of the 
tube, but that of the piece which is already in place, 
acting like an electromagnet. Beginning with a gentle 
attraction, it soon runs up, and draws the force curve to 
a tremendously steep peak, becoming a very great force 
when the distance asunder is very small. We have 
therefore in this case a totally different curve made up 


of two parts, a part for the putting in of the first half 
of the core, and a steeper part for the second; but the 
net result is, we have the same quantity of iron mag- 
netized in exactly the same manner by the same quan- 
tity of electric current running round the same amount 
of copper wire that is to say, the total amount of work 
done in these two cases is necessarily equal. Whether 
you allow the entire plunger to come in by a gentle pull 
over a long range, or whether you put the core in in two 
pieces one part with a gentle pull and the other with 
a sudden spring up at the end the total work must be 
the same; that is to say, the total area under our two 
new curves must be the same as the area under the old 
curve. The advantage, then, of this coil-and-plunger 
method of employing iron and copper is, not that it gets 
any more work out of the same expenditure of energy, 
but that it distributes the pull over a considerable range. 
It does not, however, equalize it altogether over the 
range of travel. 

A number of experimental researches have been made 
from time to time to elucidate the working of the coil- 
and-plunger. Hankel, in 1850, examined the relation 
between the pull in a given portion of the plunger and 
the exciting power. He found that, so long as the iron 
core was so thick and the exciting power so small that 
magnetization of the iron never approached saturation, 
the pull was proportional to the square of the current, 
and was also proportional to the square of the number 
of turns of wire. Putting these two facts together, we 
get the rule which is true only for an unsaturated core 
in a given position that the pull is proportional to the 

\ V t , 


square of the ampere turns. This might have been ex- 
pected, for the magnetism of the iron core will, under 
the assumptions made above, be proportional to the 
ampere turns, and the intensity of the magnetic field in 
which it is placed being also proportional to the ampere 
turns, the pull, which is the product of the magnetism 
and of the intensity of the field, ought to be propor- 
tional to the square of the ampere turns. 

Dub, who examined cores of different thicknesses, 
found the attraction to vary as the square root of the 
diameter of the core. His own experiments show that 
this is inexact, and that the force is quite as nearly pro- 
portional to the diameter as to its square root. There 
is again reason for this. The magnetic circuit consists 
largely of air paths by which the magnetic lines flow 
from one end to the other. As the main part of the 
magnetic reluctance of the circuit is that of the air, 
anything which reduces the air reluctance increases the 
magnetization, and, consequently, the pull. Now, in 
this case, the reluctance of the air paths is mainly gov- 
erned by the surface exposed by the end portions of the 
iron core. Increasing these diminishes the reluctance, 
and increases the magnetization by a corresponding 
amount. Von Waltenhofen, in 1870, compared the at- 
traction exerted by two equal (short) tubular coils on two 
iron cores, one of which was a solid cylindrical rod, and 
the other a tube of equal length and weight, and found 
the two to be more powerfully attracted. Doubtless, the 
effect of the increased service in diminishing the reluc- 
tance of the magnetic circuit explains the cause of the 



Von Feilitzsch compared the action of a tubular coil 
upon a plunger of soft iron with that exerted by the 
same coil upon a core of hard magnetized steel of equal 
dimensions. The plungers (Fig. 62) were each 10.1 cen- 
timetres long,, the coil being 
29.5 centimetres in length 
and 4.2 in diameter. The 
steel magnet showed a maxi- 
mum attraction when it had 
plunged to a depth of five 
centimetres, while the iron 
core had its maximum at a 
depth of seven centimetres, 
doubtless because its own 
magnetization went on in- 
creasing more than did that 
of the steel core. As the uni- 
form field region began at a 
depth of about eight centime- 
tres, and the cores were 10.1 
centimetres in length, one 
would expect the attracting 
force to come to zero when 
the cores had plunged in to a 
MENT ON PLUNGERS OF IRON AND depth of about 18 centime- 
tres. Asa matter of fact, the 

zero point was reached a little earlier. It will be noticed 
that the pull at the maximum was a little greater in 
the case of the iron plunger. 

The most careful researches of late years are those 
made by Dr. Theodore Bruger, in 1886. One of his re- 



searches, in which a cylindrical iron plunger was used, 
is represented by two of the curves in Fig. 63. He used 
two coils, one 3^ centimetres long, the other seven cen- 
timetres long. These are indicated in the bottom left- 
hand corner. The exciting current was a little over 
eight amperes. The cylindrical plunger was 39 centi- 



metres long. The plunger is supposed, in the diagram, 
to enter on the left, and the number of grammes of pull 
is plotted out opposite the position of the entering end 
of the plunger. As the two curves show by their steep 
peaks, the maximum pull occurs just when the end of 
the plunger begins to emerge through the coil, and the 
pull comes down to zero when the ends of the core pro- 


trude equally. In this figure the dotted curves relate to 
the use of the longer of the two coils. The height of 
the peak, with the coil of double length, is nearly four 
times as great, there being double ampere turns of ex- 
citation. In some other experiments, which are plotted 
in Fig. 64, the same core was used "with a tubular coil 13 
centimetres long. Using currents of various strengths, 
1.5 ampere, 3, 4.8, 6, or 8 amperes, the pull is of course 
different, but broadly, you get the same effect, that the 
maximum pull occurs just where the pole begins to 
come out at the far end of the tubular coil. There are 
slight differences; with the smallest amount of current 
the maximum is exactly over the end of the tube, but 
with currents rather larger the maximum point comes 
a little farther back. When the core gets well saturated, 
the force curve does not go on rising so far; it begins 
to turn over at an earlier stage, and the maximum place 
is necessarily displaced a little way back from the end 
of the tube. That was also observed by Von Walten- 
hofen when using the steel magnet. 


But now, if, instead of employing a cylindrical core, 
you employ one that is pointed, you find this completely 
alters the position of the maximum pull, for now the 
point is insufficient to carry the whole of the magnetic 
lines which are formed in the iron rod. They do not 
come out at the point, but filter through, so to speak, 
along the sides of the core. The region where the mag- 
netic lines come up through the iron into the air is no 


longer a definite "pole" at or near the end of the rod, 
but is distributed over a considerable surface; conse- 
quently when the point begins to poke its nose out, you 
still have a larger portion of iron up the tube, and the 
pull, instead of coming to a maximum at that position, 
is distributed over a wider range. I am now making 
the experiment roughly with my spring balance and a 
conical plunger, and I think you will be able to notice 
a marked difference between this case and that of the 
cylindrical plunger. The pull increases as the plunger 
enters, but the maximum is not so well defined with a 
pointed core as it is with one that is flat ended. This 
essential difference between coned plungers and cylin- 
drical ones was discovered by an engineer of the name 
of Krizik, who applied his discovery in the mechanism 
of the Pilsen arc lamps. Coned plungers were also ex- 
amined by Bruger. In Fig. 63 are given the curves that 
correspond to the use of a coned iron core, as well as 
those corresponding to the use of the cylindrical iron 
rod. You will notice that, as compared with the cylin- 
drical plunger, the coned core never gave so big a pull, 
and the maximum occurred not as the tip emerged, but 
when it got a very considerable way out on the other 
side. So it is with both the shorter and the longer coil. 
The dotted curves in Fig. 64 represent the behavior of 
a coned plunger. With the longer coil represented, and 
W 7 ith various currents, the maximum pull occurred when 
the tip had come a considerable way out; and the posi- 
tion of the maximum pull, instead of being brought 
nearer to the entering end with a high magnetizing 
current, was actually caused to occur further down. The 


range of action became extended with large currents as 
compared with small ones. Bruger also investigated 
the case of cores of very irregular shapes, resembling, 
for example, the shank of a screw-driver, and found a 
very curious and irregular force curve. There is a good 
deal more yet to be done, I fancy, in examining this 
question of distributing the pull on an attracted core by 
altering the shape of it, but Bruger has shown us the 
way, and we ought not to find very much difficulty in 
following him. 


Another way of altering the distribution of the pull is 
to alter the distribution of the wire on the coil. In- 
stead of having a coned core use a coned coil, the wind- 
ing being heaped up thicker at one end than at the 
other. Such a coil, wound in steps of increasing thick- 
ness, has been used for some years by G-aiffe in his arc 
lamp; it has also been patented in Germany by Leu- 
pold. M. Treve has made the suggestion to employ an 
iron wire coil, so to utilize the magnetism of the iron 
that is carrying the current. Treve declares that such 
coils possess for an equal current four times the pulling 
power. I doubt whether that is so; but even if it were, 
we must remember that to drive any given current 
through an iron wire, instead of a copper wire of the 
same bulk, implies that we must force the current 
through six times the resistance; and, therefore, we 
shall have to employ six times the horse power to drive 
the same current through the iron wire coil, so that 


there is really no gain. Again, a suggestion has been 
made to inclose in an iron jacket the coil employed in 
this way. Iron-clad solenoids have been employed from 
time to time. But they do not increase the range of 
action. What they do is to tend to prevent the falling 
off of the internal pull at the region within the mouth 
of the coil. It equalizes the internal pull at the expense 
of all external action. An iron-clad solenoid has prac- 
tically no attraction at all on anything outside of it, not 
even on an iron core placed at a distance of half a diam- 
eter of the aperture; it is only when the core is inside 
the tube that the attraction begins, and the magnetiz- 
ing power is practically uniform from end to end. Last 
year I wished to make use of this property for some 
experiments on the action of magnetism on light, and 
for that purpose I had built, by Messrs. Paterson and 
Cooper, this powerful coil, which is provided with a 
tubular iron jacket outside, and a thick iron disc per- 
forated by a central hole covering each end. The mag- 
netic circuit around the exterior of the coil is practically 
completed with soft iron. With this coil, one may take 
it, there is an absolutely uniform magnetic field from 
one end of the tube to the other; not falling off at the 
ends as it would do if the magnetic circuit had simply 
an air return. The whole of the ampere turns of ex- 
citing power are employed in magnetizing the central 
space, in which therefore the actions are very powerful 
and uniform. The coil and its uses were described in 
my lecture last year at the Royal Institution on "Opti- 
cal Torque/' 



In one variety of the coil-and-plunger mechanism a 
second coil is wound on the plunger. Hjorth used this 
modification, and the same thing has been employed in 
several arc lamps. There is a series of drawings upon 
this wall depicting the mechanism of ahout a dozen 
different forms of arc lamp, all made by Messrs. Pater- 
son and Cooper. In one of these there is a plunger 
with a coil on it drawn into a tubular coil, the current 
flowing successively through both coils. In another 
there are two separate coils in separate circuits, one of 
thin wire and one of thick, one being connected in 
series with the arc, and one in shunt. 


There is a third drawing here, showing the arrange- 
ment which was originally introduced by Siemens, 
wherein a plunger is drawn at one end into the coil that 
is in the main circuit, and at the other end into a coil 
that is in shunt. That differential arrangement has 
certain peculiar properties of which I must not now 
stop to speak in detail. It is obvious that where one 
core plunges its opposite ends into two coils, the mag- 
netization will depend on both coils, and the resultant 
pull will not be simply the difference between the pull 
of the two coils acting each separately. There is, how- 
ever, another differential arrangement, used in the 
Brockie-Pell and other arc lamps, in which there are 
two separate plungers attached to the two ends of a 
see-saw lever. In this case the two magnetizing actions 


are separate. In a third differential arrangement there 
is but one plunger and one tubular bobbin, upon which 
are wound the two coils, differentially, so that the 
action on the plunger is simply due to the difference 
between the ampere turns circulating in the two sepa- 
rate wires. 


When one abandons iron altogether, and merely uses 
two tubular coils, one of wide diameter and another of 
narrower diameter, capable of entering into the former, 
and passes electric currents through both of them, if 
the currents are circulating in the same fashion through 
both of them they will be drawn into one another. 
This arrangement has also been used in arc lamps. 
The parallel currents attract one another inversely, not 
as the square of the distance, but approximately as the 
distance. This is one of those little details about which 
it is as well to be clear. About once a year some kind 
friend from a distance writes to me pointing out a little 
slip that he says occurs in my book on electricity, in 
the passage where I am speaking about the attraction 
of parallel wires. I have made the terrible blunder of 
leaving out the word square; for I say the attraction 
varies inversely as the distance, and my readers are 
kind enough to correct me. Now when I wrote that 
passage I considered carefully what I had to write, and 
the attraction does not vary inversely as the square of 
the distance, because two parallel wires dp not act on 
one another as two points. They act as two straight 
lines or two parallel lines, and the attraction between 



two parallel lines of current, or two parallel lines of 
magnetism, or two parallel lines of anything else that 
can attract, will not act inversely as the square, but 
simply inversely as the distance in between. 


Now this property of the coil-and-plunger of extend- 
ing the range of action has been adopted in various 
ways by inventors whose object was to try and make 

electromagnets with a sort 
of intermediate range. For 
certain purposes it is desir- 
able to construct an electro- 
magnet which, while having 
the powerful pull of the 
electromagnet, should have 
over its limited range of 
action a more equable pull, 
resembling in this respect 
the equalizing of range of 
the coil-and-plunger. Some 
of these intermediate forms 
of apparatus are shown in 
the following diagrams. 
Here (Fig. 65) is a peculiar 
form of electromagnet; it combines some of the fea- 
tures of the iron-clad electromagnet with those of the 
movable plunger; it has a limited range of action, but 
is of great power over that range, owing to its excellent 
magnetic circuit. It was invented in 1870 by Stevens 
and Hardy for use in an electric motor for running 




sewing machines. A very similar form is used in Wes- 
ton's arc lamp. A form of plunger electromagnet in- 
vented by Holroyd Smith in 1877 resembles Fig. 65 in- 
verted, the coil being surrounded by an iron jacket, 
while a plunger furnished at the top with an iron disc 
descends down the central tube to meet the iron at the 

Then there is another variety, of which I was able to 
show an example last week by the kindness of the 
Brush Company, namely, 
the plunger electromagnet 
employed in the Brush arc 
lamps. A couple of tubular 
coils receive each an iron 
plunger, connected together 
by a yoke; while above, the 
magnetic circuit is partially 
completed by the sheet of 
iron which forms part of the 

inclosing box. You have FlG - SG.-ELECTHOMAGNET OF BRUSH 


here, also, the advantage of 

a fairly complete magnetic circuit, together with a com- 
paratively long travel of the plunger and coil. It is a 
fair compromise between the two ways of working. 
The pull is not, however, in any of these forms, equal 
all along the whole range of travel; it increases as the 
magnetic circuit becomes more complete. 

There are several other intermediate forms. For ex- 
ample, one inventor, Gaiser, employs a horseshoe elec- 
tromagnet, the cores of which protrude a good distance 
beyond the coils, and for an armature he employs a 



piece of sheet iron, bent round so as to make at its ends 
two tubes, which inclose the poles, and are drawn down 
over them. Contrast with this design one of much 
earlier date by an engineer, Roloff, who made his elec- 
tromagnets with iron cores not standing out, but sunk 
below the level of the ends of the coils, while the arma- 
ture was furnished with little extensions that passed 
down into these projecting tubular ends of the coils. 
Some arc lamps have magnets of 
precisely that form, with a short 
plunger entering a tubular coil, 
and met half-way down by a short 
fixed core inside the tube. 

Here (Fig. 67) is one form of 
tubular iron-clad electromagnet 
that deserves a little more atten- 
tion, being the one used by Messrs. 
Ayrton and Perry in 1882; a coil 
has an iron jacket round it, and 
also an annular iron disc across the 
top, and an annular iron disc across 
the bottom, there being also a short 
internal tube of iron extending a little way down from 
the top, almost meeting another short internal tube of 
iron coming up from the bottom. The magnetic effect 
of the inclosed copper coil is concentrated within an 
extremely short space, between the ends of the internal 
tubes, where there is a wonderfully strong uniform field. 
The range of action you can alter just as you please 
in the construction by shortening or lengthening the 
internal tubes. An iron rod inserted below is drawn 



with great power and equality of pull over the range 
from one end to the other of these internal tubes. 


In dealing with the action of tubular coils upon iron 
cores, I showed how, when a very short core is placed 
in a uniform magnetic field, it is not drawn in either 
direction. The most extreme case is where a small 
sphere of soft iron is employed. Such a sphere, if 
placed in even the most powerful magnetic field, does 
not tend to move in any direction if the field is truly 
uniform. If the field is not uniform, then the iron 
sphere always tends to move from the place where the 
field is weak to a place where the field is stronger. A 
ball of bismuth or one of copper tends, on the contrary, 
to move from a place where the field is strong to a 
place where the field is weaker. This is the explanation 
of the actions called " dia-magnetic," which were at one 
time erroneously attributed to a supposed dia-magnetic 
polarity opposite in kind to the ordinary magnetic 
polarity. A simple way of stating the facts is to say 
that a small sphere of iron tends to move up the slope 
of a magnetic field, with a force proportional to that 
slope; while (in air) a sphere of bismuth or one of 
copper tends, with a feeble force, to move down that 
slope; any small piece of soft iron a short cylinder, 
for example shows the same kind of behavior as a 
small sphere. In some of Ayrton and Perry's coiled- 
ribbon ampere-meters and voltmeters, and in some of 
Sir William Thomson's current meters, this principle 
is applied. 



An important suggestion was made by Page, about 
1850, when he designed a form of coil-and-plunger hav- 
ing a travel of indefinitely long range. The coiled tube 
instead of consisting merely of one coil, excited simul- 
taneously throughout its whole length by the current, 
was constructed in a number of separate sections or 
short tubes, associated together end to end, and fur- 
nished with means for turning on the electric current 
into any of the sections separately. Suppose an iron 
core to be just entering into any section, the current is 
turned on in that section, and as the end of the core passes 
through it the current is then turned on in the section 
next ahead. In this way an attraction may be kept up 
along a tube of indefinite length. Page constructed an 
electric motor on this plan, which was later revived by 
Du Moncel, and again by Marcel Deprez in his electric 
" hammer/' 


The mention of this mode of winding in sections 
leads me to say a few final words about winding in 
general. All ordinary coils, whether tubular or pro- 
vided with fixed cores, are wound in layers of alternate 
right-handed and left-handed spirals. In a preceding 
lecture I mentioned the mistaken notion, now dis- 
proved, that there is any gain in making all the spirals 
right-handed or all left-handed. For one particular 
case there is an advantage in winding a coil in sections; 
that is to say, in placing partitions or cloisons at inter- 


vals along the bobbin, and winding the wire so as to 
fill up each of the successive spaces between the parti- 
tions before passing on from one space to the next. 
The case in which this construction is advantageous is 
the unusual case of coils that are to be used with cur- 
rents supplied at very high potentials. For when cur- 
rents are supplied at very high potentials there is a 
very great tension exerted on the insulating material, 
tending to pierce it with a spark. By winding a coil in 
cloisons, however, there is never so great a difference of 
potential between the windings on two adjacent layers 
as there would be if the layers were wound from end to 
end of the whole length of coil. Consequently, there is 
never so great a tension on the insulating material be- 
tween the layers, and a coil so wound is less likely to be 
injured by the occurrence of a spark. 

Another variety of winding has been suggested, 
namely, to employ in the coils a wire of graduated thick- 
ness. It has been shown by Sir William Thomson to 
be advantageous in the construction of coils of galva- 
nometers to use for the inner coils of small diameter a 
thin wire; then, as the diameter of the windings in- 
creases, a thicker wire; the thickest wire being used on 
the outermost layers; the gauge being thus propor- 
tioned to the diameter of the windings. But it by no 
means follows that the plan of using graded wire, which 
is satisfactory for galvanometer coils, is necessarily good 
for electromagnets. In designing electromagnets it is 
necessary to consider the means of getting rid of heat ; 
and it is obvious that the outer layers are those which 
are in the most favorable position for getting rid of 


this heat. Experience shows that the under layers of 
coils of electromagnets always attain a higher tempera- 
ture than those at the surface. If, therefore, the inner 
layers were to he wound with finer wire, offering higher 
resistance, and generating more heat than the outer 
layers, this tendency to overheating would be still 
more accentuated. Indeed, it would seem wise rather 
to reverse the galvanometer plan, and wind electromag- 
nets with wires that are stouter on the inner layers and 
finer on the outer layers. 

Yet another mode of winding is to employ several 
wires united in parallel, a separate wire being used for 
each layer, their anterior extremities being all soldered 
together at one end of the coil, and their posterior ex- 
tremities being all soldered together at the other. 
Magnetically, this mode of winding presents not the 
slightest advantage over winding with a single stout 
wire of equivalent section. But it has lately been dis- 
covered that this mode of winding with multiple wire 
possesses one incidental advantage, namely that its use 
diminishes the tendency to sparking which occurs at 
break of circuit. 


I now pass to the means which have been suggested 
for extending the range of motion, or of modifying its 
amount at different parts of the range, so as to equalize 
the very unequable pull. There are several such de- 
vices, some electrical, others purely mechanical, others 
electro-mechanical. First, there is an electrical method. 
Andre proposed that, as soon as the armature has begun 


to move nearer, and comes to the place where it is at- 
tracted more strongly, it is automatically to make a 
contact, which will shunt off part of the current and 
make the magnetism less powerful. Burnett proposed 
another means; a number of separate electromagnets 
acting on one armature, but as the latter approached 
these electromagnets were one after the other cut out of 
the circuit. I need not say the advantages of that 
method are very hypothetical. Then there is another 
method which has been used many times with very 
great success, the method of allowing the motion of the 
armature to occur obliquely, it being mechanically con- 
strained so as to move past, instead of toward the 
pole. When the armature is pulled thus obliquely, the 
pull will be distributed over a definite wider range. 
Here is a little motor made on that very plan. A num- 
ber of pieces of iron set on the periphery of a wheel are 
successively attracted up sideways. An automatic de- 
vice breaks the circuit as every piece of iron comes 
near, just at the moment when it gets over the poles, 
and the current being cut off, it flies on beyond and 
another piece comes up, is also attracted in the same 
way, and then allowed to pass. A large number of toy 
motors have been made from time to time on this plan. 
I believe Wheatstone was the first to devise the method 
of oblique approach about the year 1841. He made 
many little electromagnetic motors, the armatures of 
which were in some cases solid rims of iron arranged 
as a sort of wheel, with two or more zigzag internal 
teeth, offering oblique surfaces to the attraction of an 
electromagnet. Such little motors are often now used 


for spinning Geissler's vacuum tubes. In these motors 
the iron rim is fixed and the electromagnet rotates. 
The pole of the electromagnet finds itself a certain dis- 
tance away from the iron ring; it tries to get nearer. 
The only way it can get nearer is by swinging round, 
and so it gradually approaches, and as it approaches 
the place where it is nearest to the internal projection 
of the rim the current is cut off, and it swings further. 
This mode may be likened to a cam in a mechanical 
movement. It is, in fact, nothing else than an electro- 
magnetic cam. There are other devices too, which are 
more like electromagnetic linkage. If you curve the 
poles or shape them out, you may obtain actions which 
are like that of a wedge on an inclined plane. There 
is an electromagnet in one of Paterson and Cooper's arc 
lamps wherein the pole-piece, coming out below the 
magnet, has a very peculiar shape, and the armature is 
so pivoted with respect to the magnet, that as the arma- 
ture approaches the core as a whole its surface recedes 
from that of the pole-piece, the effect being that the 
pull is equalized over a considerable range of motion. 
There is a somewhat similar device in De Puydt's pat- 
tern of arc lamp. 

Here is another device for oblique approach, made by 
Froment. In the gap in the circuit of the magnet a 
sort of iron wedge is put in, which is not attracted 
squarely to either face, but comes in laterally between 
guides. Another of Froment's equalizers, or distribu- 
tors, consists of a parallel motion attachment for the 
armature, so that oblique approach may take place, 
without actual contact, Here (Fig. 68) is another me- 



chanical method of equalizing devised by Froment, and 
used by Le Eoux. You know the Stanhope lever, the 
object of which is to transform a weak force along a 
considerable range into a powerful force of short range. 
Here we use it backward. The armature itself, which 



is attracted with a powerful force of short range, is at- 
tached to the lower end of the Stanhope lever, and the 
arm attached to the knee of the lever will deliver a dis- 
tributed force over quite a different range. One way, 
not of equalizing the actual motion over the range, but 
of counterbalancing the variable attractive force, is to 
employ a spring instead of gravity to control the arma- 


ture. So far back as 1838, Edward Davy, in one of his 
telegraphic patents, described the use of a spring (Fig. 
69) to hold back the armature. Davy preceded Morse 
in the use of a spring to pull back the armature. There 
is a way of making a spring act against an armature 
more stiffly as the pull gets greater. In this method 
there is a spring with various set screws set up against 


it, and which come into action at different ranges, so as 
to alter the stiffness of the spring, making it virtually 
stiffer as the armature approaches the poles. Yet an- 
other method is to employ, as the famous conjurer Eobert 
Houdin did, a rocking lever. Fig. 70 depicts one of 
Robert Houdin's equalizers. The pull of the electro- 
magnet on the armature acts on a curved lever which 
works against a second one, the point of application of 
force between the one and the other altering with their 



position. When the armature is far away from the 
pole, the leverage of the first lever on the second lever 
is great. When the armature gets near, the leverage of 
the first lever on the second is comparatively small. 
This employment of the rocking lever was adopted from 
Houdin by Duboscq, and put into the Duboscq arc lamp, 
where the regulating mechanism at the bottom of the 
lamp contains a rocking lever. Here upon the lecture 
table is a Duboscq arc lamp. In this pattern (Fig. 71), 


one lever, B, which is curved, plays against another, A, 
which is straight. A similar mechanism is used for 
equalizing the action in the Serrin arc lamp, where one 
of the springs that holds up the jointed parallelogram 
frame is applied at the end of a rocking lever to equalize 
the pull of the regulating electromagnet. In this lamp 
there is also introduced the principle of oblique approach; 
for the armature of the electromagnet is not allowed to 
travel straight toward the poles of the magnet, but is 
pulled up obliquely past it. 


Another device for equalizing the pull was used by 
Wheatstone in the step-by-step telegraph in 1840. A 
hole is pierced in the armature, and the end of the core 
is formed into a projecting cone, which passes through 
the aperture of the armature, thereby securing a more 
equable force and a longer range. The same device has 
reappeared in recent years in the form of electromagnet 
used in the Thomson-Houston arc lamp, and in the 
automatic regulator of the same firm. 



We must now turn our attention to one class of elec- 
tromagnetic mechanism -which ought to be carefully 
distinguished from the rest. It is that class in which, 
in addition to the ordinary electromagnet, a permanent 
magnet is employed. Such an arrangement is generally 
referred to as a polarized mechanism. The objects for 
which the permanent magnet is introduced into the 
mechanism appear to be in different cases quite differ- 
ent. I am not sure whether this is clearly recognized, 
or whether a clear distinction has even been drawn be- 
tween three entirely separate purposes in the use of a 
permanent magnet in combination with an electromag- 
net. The first purpose is to secure unidirectionality of 
motion; the second is to increase the rapidity of action 
and of sensitiveness to small currents; the third to aug- 
ment the mechanical action of the current. 

(a.) Unidirectionality of Motion. In an ordinary elec- 
tromagnet it does not matter which way the current 
circulates; no matter whether the pole is north or 


south, the armature is pulled, and on reversing the cur- 
rent the armature is also pulled. There is a rather 
curious old experiment which Sturgeon and Henry 
showed, that if you have an electromagnet with a big 
weight hanging on it, and you suddenly reverse the 
current, you reverse the magnetism, but it still holds 
the weight up; it does not drop. It has not time to 
drop before the magnet is charged up again with mag- 
netic lines the other way on. Whichever way the mag- 
netism traverses the ordinary soft iron electromagnet, 
the armature is pulled. But if the armature is itself a 
permanent magnet of steel, it will be pulled when the 
poles are of one sort, and pushed when the poles are 
reversed that is to say, by employing a polarized arma- 
ture you can secure unidirectionality of motion in cor- 
respondence with the current. One immediate applica- 
tion of this fact for telegraphic purposes is that of 
duplex telegraphy. You can send two messages at the 
same time and in the same direction to two different 
sets of instruments, one set having ordinary electro- 
magnets, with a spring behind the armature of soft iron, 
which will act simply independently of the direction of 
the current, depending only on its strength and dura- 
tion; and another set having electromagnets with polar- 
ized armatures, which will be affected not by the strength 
of the current, but by the direction of it. Accord- 
ingly, two completely different sets of messages may be 
sent through that line in the same direction at the same 

Another mode of constructing a polarized device is to 
attach the cores of the electromagnet to a steel magnet, 


which imparts to them an initial magnetization. Such 
initially magnetized electromagnets were used by Brett 
in 1848 and by Hjorth hi 1850. A patent for a similar 
device was applied for in 1870 by !Sir William Thomson 
and refused by the Patent Office. In 1871 S. A. Varley 
patented an electromagnet having a core of steel wires 
united at their ends. 

Wheatstone used a polarized apparatus consisting of 
an electromagnet acting on a magnetized needle. He 
patented, in fact, in 1845, the use of a needle perma- 
nently magnetized to be attracted one way or the other 
between the poles of an electromagnet. Sturgeon had 
described the very same device in the Annals of Elec- 
tricity in 1840. Gloesner claims to have invented the 
substitution of permanent magnets for mere armatures 
in 1842. In using polarized apparatus it is necessary to 
work, not with a simple current that is turned off and 
on, but with reversed currents. Sending a current one 
way will make the moving part move in one direction; 
reversing the current makes it go over to the other side. 
The mechanism of that particular kind of electric bell 
that is used with magneto-electric calling apparatus 
furnishes an excellent example of a polarized construc- 
tion. With these bells no battery is used; but there is 
a little alternate current dynamo, worked by a crank. 
The alternate currents cause the pivoted armature in 
the bell to oscillate to right and left alternately, and so 
throw the little hammer to and fro between the two 

(>.) Rapidity and Sensitiveness of Action. For relay 
work polarized relays are often employed, and have been 


for many years. Here on the table is one of the post- 
office pattern of standard relay, having a steel magnet 
to give magnetism permanently to a little tongue or 
armature which moves between the poles of an electro- 
magnet that does the work of receiving the signals. In 
this particular case the tongue of the polarized relay 
works between two stops, and the range of motion is made 
very small in order that the apparatus may respond to 
very small currents. At first sight it is not very appar- 
ent why putting a permanent magnet into a thing should 
make it any more sensitive. Why should permanent 
magnetism secure rapidity of working ? Without know- 
ing anything more, inventors will tell you that the pres- 
ence of a permanent magnet increases the rapidity with 
which it will work. You might suppose that perma- 
nent magnetism is something to be avoided in the cores 
of your working electromagnets, otherwise the arma- 
tures would remain stuck to the poles when once they 
had been attracted up. Kesidual magnetism would, in- 
deed, hinder the working unless you have so arranged 
matters that it shall be actually helpful to you. Now 
for many years it was supposed that permanent mag- 
netism in the electromagnet was anything but a source 
of help. It was supposed to be an unmitigated nuisance, 
to be got rid of by all available means, until, in 1855, 
Hughes showed us how very advantageous it was to have 
permanent magnetism in the cores of the electromag- 
net. Here (Fig. 51), is the drawing of Hughes' magnet 
to which I referred in Lecture III. A compound per- 
manent magnet of horseshoe shape is provided with coils 
on its pole-pieces, and there is a short armature on the 


top attached to a pivoted lever and a counteracting 
spring. The function of this arrangement is as follows : 
That spring is so set as to tend to detach the armature, 
but the permanent magnet has just enough magnetism 
to hold the armature on. You can, by screwing up a 
little screw behind the spring, adjust these two con- 
tending forces> so that they are in the nicest possible 
balance; the armature held on by the magnetism, and 
the spring just not able to pull it off. If, now, when 
these two actions are so nearly balanced you send an 
electric current round the coils, if the electric current 
goes one way round it just weakens the magnetism 
enough for the spring to gain the victory, and up goes 
the armature. This apparatus then acts by letting the 
armature off when the balance is upset by the electric 
current; and it is capable of responding to extremely 
small currents. Of course, the armature has to be put 
on again mechanically, and in Hughes' type-writing 
telegraph instruments it is put on mechanically between 
each signal and the next following one. The arrange- 
ment constitutes a distinctive piece of electromagnetic 

(c.) Augmenting Mechanical Action of Current. The 
third purpose of a permanent magnet, to secure a greater 
mechanical action of the varying current, is closely 
bound up with the preceding purpose of securing sen- 
sitiveness of action. It is for this purpose that it is used 
in telephone receivers; it increases the mechanical ac- 
tion of the current, and therefore makes the receiver 
more sensitive. For a long time this was not at all 
clear to me, indeed I made experiments to see how far 


it was due to any variation in the magnetic permeability 
of iron at different stages of magnetization, for I found 
that this had something to do with it, but I was quite 
sure it was not all. Prof. George Forbes gave me 
the clue to the true explanation; it lies in the law of 
traction with which you are now familiar, that the pull 
between a magnet and its armature is proportional to 
the square of the number of magnetic lines that come 
into action. If we take N, the number of magnetic 
lines that are acting through a given area>, then to the 
square of that the pull will be proportional. If we 
have a certain number of lines, N, coming permanently 
to the armature, the pull is proportional to N 2 . Sup- 
pose the magnetism now to be altered say made a little 
more; and the increment be called dN; so that the 
whole number is now N+^N. The pull will now be 
proportional to the square of that quantity. It is evi- 
dent that the motion will be proportional to the differ- 
ence between the former pull and the latter pull. So 
we will write out the square of N+^N and the square 
of N and take the difference. 

Increased pull, proportional to N 2 +2 N<#N+dN 2 ; 

Initial pull, proportional to N 2 

Subtracting; difference is 2 N^N+^N 2 . 

^e may neglect the last term, as it is small com- 
pared with the other. So we have, finally, that the 
change of pull is proportional to 2 N^N. The altera- 
tion of pull between the initial magnetism and the 
initial magnetism with the additional magnetism we 
have given to it turns out to be proportional not simply 


to the change of magnetism, but also to the initial num- 
ber N, that goes through it to begin with. The more 
powerful the pull to begin with, the greater is the 
change of pull when you produce a small change in the 
number of magnetic lines. That is why you have this 
greater sensitiveness of action when using Hughes* elec- 
tromagnets, and greater mechanical effect as the result 
of applying permanent magnetism to the electromagnets 
of telephone receivers. 


There are some other kinds of electromagnetic mech- 
anism to which I must briefly invite your attention 
as forming an important part of this great subject. 
Of one of these the mention of permanent magnets re- 
minds me. 


A coil traversed by an electric current experiences 
mechanical forces if it lies in a magnetic field, the force 
being proportional to the intensity of the field. Of this 
principle the mechanism of Sir Wm. Thomson's siphon 
recorder is a well-known example. Also those galva- 
nometers which have for their essential part a movable 
coil suspended between the poles of a permanent mag- 
net, of which the earliest example is that of Robertson 
("Encyclopaedia Britannica," ed. viii., 1855), and of 
which Maxwell's suggestion, afterward realized by d'Ar- 
sonval, is the most modern. Siemens has constructed 
a relay on a similar plan, 



There are a few curious pieces of apparatus devised 
for increasing adherence electrornagnetically between 
two things. Here is an old device of Nickles, who 
thought he would make a new kind of rolling gear. 
Whether it was a railway wheel on a line, or whether it 


was going to be an ordinary wheel gearing, communi- 
cation of motion was to be made from one wheel to an- 
other, not by cogs or by the mere adherence of ordinary 
friction, but by magnetic adherence. In Fig. 72 there 
are shown two iron wheels rolling on one another, with 
a sort of electromagnetic jacket around them, consisting 
of an electric current circulating in a coil, and causing 



them to attract one another and stick together with 
magnetic adherence. In Nickles' little book on the 
subject there are a great number of devices of this kind 
described, including a magnetic brake for braking rail- 
way wagons, engines, and carriages, applying electro- 
magnets either to the wheels or else to the line, to stop 
the motion whenever desired. The notion of using 
an electromagnetic brake has been revived quite recently 
in a much better form by Prof. Geo. Forbes and Mr. 

Timmis, whose particular 
form of electromagnet, 
shown in Fig. 73, is pecu- 
liarly interesting, being a 
better design than any I 
have ever seen for securing 
powerful magnetic traction 
for a given weight of iron 
and copper. The magnet 
is a peculiar one; it is rep- 
resented here as cut away to show the internal con- 
struction. There is a sort of horseshoe made of one 
grooved rim, the whole circle of coil being laid imbed- 
ded in the groove. The armature is a ring which is 
attracted down all round, so that you have an extremely 
compact magnetic circuit around the copper wire at 
every point. The magnet part is attached to the frame 
of the wagon or carriage, and the ring-armature is at- 
tached to the wheel or to its axis. On switching on the 
electric current the rim is powerfully pulled, and braked 
against the polar surface of the electromagnet. 

Forbes' arrangement appears to be certainly the best 




yet thought of for putting a magnetic brake to the 
wheels of a railway train. 

Another, but quite distinct, piece of mechanism de- 
pending on electromagnetic adherence is the magnetic 
clutch employed in Gulcher's arc lamp. 


Then there are a few pieces of mechanism which de- 
pend on repulsion. In 1850 a little device was patented 
by Brown and Williams, consisting, as shown in Fig. 



74, of an electromagnet which repelled part of itself. 
The coil is simply wound on a hollow tube, and inside 
the coil is a piece, B, of iron, bent as the segment of a 
cylinder to fit in, going from one end to the other. 
Another little iron piece, A, also shaped as the segment 
of a tube, is pivoted in the axis of the coil. When 
these are magnetized one tends to move away from the 
other, they being both of the same polarity. Of late 
there have been many ampere-meters and voltmeters 


made on this plan of producing repulsion between the 
parallel cores. 

Here (Fig. 75) is another device of recent date, due to 
Maikoff and De Kabath. Two cores of iron, not quite 
parallel, pivoted at the bottom, pass up through a tubiu 
lar coil. When both are magnetized, instead of attract- 
ing one another, they open out; they tend to set them- 
selves along the magnetic lines through that tube. The 
cores, being wide open at the bo.ttom, tend to oper also 
at the top. 


Then there is a large class of mechanisms about which 
a whole chapter might be written, namely, those in 
which vibration is maintained electromagnetically. The 
armature of an electromagnet is caused to approach and 
recede alternately with a vibrating motion, the current 
being automatically cut off and turned on again by a 
self-acting brake. The electromagnetic vibrator is one 
of the cleverest things ever devised. The first vibrat- 
ing electromagnetic mechanism ever made was exhibited 
here in this room in 1824 by its inventor, an English- 
man named James Marsh. It consisted of a pendulum 
vibrating automatically between the poles of a perma- 
nent magnet. Later, a number of other vibrating de- 
vices were produced by Wagner, Neef, Froment, and 
others. Most important of all is the mechanism of the 
common electric trembling bell, invented by a man 
whose very name appears to be quite forgotten John 
Mirand. How many of the millions of people who use 
electric bells know the name of the man who invented 


them ? John Mirand, in the year 1850, put the electric 
bell practically into the same form in which it has heen 
employed from that day to this. The vibrating ham- 
mer, the familiar push-button,, the indicator or annun- 
ciator, are all of his devising, and may be seen depicted 
in the specification of his British patent, just as they 
came from his hand. 

Time alone precludes me from dealing minutely with 
these vibrators, and particularly with the recent work 
of Mercadier and that of Langdon-Davies, whose re- 
searches have put a new aspect on the possibilities of 
harmonic telegraphy. Langdon-Davies' rate governor 
is the most recent and perfect form of electromagnetic 


Upon the table here are a number of patterns of elec- 
tric bells, and a number also of the electro-mechanical 
movements or devices employed in electric bell work, 
some of which form admirable illustrations of the vari- 
ous principles that 1 have been laying down. Here is 
an iron-clad electromagnet; here a tripolar magnet; 
here a series of pendulum motions of various kinds; 
here is an example of oblique pull; here is Jensen's in- 
dicator, with lateral pull; here is Moseley's indicator, 
with a co il-and-pl unger, iron-clad; here is a clever de- 
vice in which a disc is drawn up to better the magnetic 
circuit. Here, again, is Thorpe's semaphore indicator, 
one of the neatest little pieces of apparatus, with a sin- 
gle central core surrounded by a coil, while a little strip 
of iron coming round from behind serves to complete 


the circuit all save a little gap. Over the gap stands 
that which is to be attracted, a flat disc of iron, which, 
when it is attracted, unlatches another disc of brass 
which forthwith falls down. It is an extremely effect- 
ive, very sensitive, and very inexpensive form of annun- 
ciator. The next two are pieces of polarized mechanism 
having a motion directed to one side or the other, ac- 
cording to the direction of the current. From the 
backboard projects a small straight electromagnet. 
Over it is pivoted a small arched steel magnet, perma- 
nently magnetized, to which is attached a small signal 
lever bearing a red disc. If there is a current flowing 
one way then the magnet that straddles over the pole of 
the electromagnet will be drawn over in one direction. 
If I now reverse the current the electromagnet attracts 
the other pole of the curved magnet. Hence this 
mechanism allows of an electrical replacement without 
compelling the attendant to walk up to the indicator 
board. The polarized apparatus for indicators has this 
advantage, that you can have electrical as distinguished 
from mechanical replacement. 


The rapid survey of electromagnetic mechanisms in 
general has necessarily been very hurried and imperfect. 
The study of it is just as important to the electrical 
engineer as is the study of mechanical mechanism to 
the mechanical engineer. Incomplete as is the present 
treatment of the subject, it may sufficiently indicate to 
other workers useful lines of progress, and so fitly be 
appended to these lectures on. the electromagnet. In a 


very few years we may expect the introduction into all 
large engineering shops of electromagnetic tools. On a 
small scale, for driving dental appliances, electromag- 
netic engines have long been used. Large machine 
tools, electromagnetically worked, have already begun 
to make their appearance. Some such were shown at 
the Crystal Palace, in 1881, by Mr. Latimer Clark, and 
more recently Mr. Rowan, of Glasgow, has devised a 
number of more derek>ped forms of electromagnetic 


It now remains for me to speak briefly of the sup- 
pression of sparks. There are some half-dozen differ- 
ent ways of trying to get rid of the sparking that occurs 
in the breaking of an electric circuit whenever there 
are electromagnets in that circuit. Many attempts have 
been made to try and get rid of this evil. For instance, 
one inventor employs an air blast to blow out the spark 
just at the moment it occurs. Another causes the spark 
to occur under a liquid. Another wipes it out with a 
brush of asbestos cloth that comes immediately behind 
the wire and rubs out the spark. Another puts on a 
condenser to try and store up the energy. Another tries 
to put on a long thin wire or a high resistance of liquid, 
or something of that kind, to provide an alternate path 
for the spark, instead of jumping across the air and 
burning the contacts. There exist some half-score, at 
any rate, of that kind of device. But there are devices 
that I have thought it worth while to examine and ex- 
periment upon, because they depend merely upon the 


mode of construction adopted in the building of the 
electromagnet, and they have each their own qualities. 
I have here five straight electromagnets, all wound on 
bobbins the same size, for which we shall use the same 
iron core and the same current for all. They are all 
made, not only with bobbins of the same size, but their 
coils consist as nearly as possible of the same weight of 
wire. The first one is wound in the ordinary way; the 
second one has a sheath of copper wound round the in- 
terior of the bobbin before any wire is put on. This 
was a device, I believe, of the late Mr. C. F. Varley, and 
is also used in the field magnets of Brush dynamos. The 
function of the copper sheath is to allow induced cur- 
rent to occur, which will retard the fall of magnetism, 
and damp down the tendency to spark. The third one 
is an attempt to carry out that principle still further. 
This is due to an American of the name of Paine, and 
has been revived of late years by Dr. Aron, of Berlin. 
After winding each layer of the coil, a sheath of metal 
foil is interposed so as to kill the induction from layer 
to layer. The fourth one is the best device hitherto 
used, namely, that of differential winding, having two 
coils connected so that the current goes opposite ways. 
When equal currents flow in both circuits there is no 
magnetism. If you break the circuit of either of the 
two wires the core at once becomes magnetized. You 
get magnetism on breaking, you destroy magnetism on 
making the circuit; it is just the inverse case to that 
of the ordinary electromagnet. There the spark occurs 
when magnetism disappears, but here, since the mag- 
netism disappears when you make the circuit, you do 


not get any spark at make, because the circuit is already 
made. You do not get any at break, because at break 
there is no magnetism. The fifth and last of these elec- 
tromagnets is wound according to a plan devised by Mr. 
Langdon-Davies, to which I alluded in the middle of 
this lecture, the bobbin being wound with a number of 
separate coils in parallel with one another, each layer 
being a separate wire, the separate ends of all the layers 
being finally joined up. In this case there are 15 sepa- 
rate circuits; the time-constants of them are different, 
because, owing to the fact that these coils are of differ- 
ent diameters, the coefficient of self-induction of the 
outer layers is rather less, and their resistance, because 
of the larger size, rather greater than those of the inner 
layers. The result is that instead of the extra current 
running out all at the same time, it runs out at differ- 
ent times for these 15 coils. The total electromotive- 
force of self-induction never rises so high and it is un- 
able to jump a large air-gap, or give the same bright 
spark as the ordinary electromagnet would give. We 
will now experiment with these coils. The differential 
winding gives absolutely no spark at all, and second in 
merit comes No. 5, with the multiple wire winding. 
Third in merit comes the coil with intervening layers 
of foil. The fourth is that with copper sheath. Last 
of all, the electromagnet with ordinary winding. 


Now let me conclude by returning to my starting- 
point the invention of the electromagnet by William 
Sturgeon. Naturally you would be glacL to see the 


counterfeit presentment of the features of so remark- 
able a man, of one so worthy to be remembered among 
distinguished electricians and great inventors. Your 
disappointment cannot be greater than mine when I 
tell you that all my efforts to procure a portrait of the 
deceased inventor have been unavailing. Only this I 
have been able to learn as the result of numerous in- 
quiries; that an oil-painting of him existed a few years 
ago in the possession of his only daughter, then resident 
in Manchester, whose address is now, unfortunately, 
unknown. But if his face must remain unknown to us, 
we shall none the less proudly concur in honoring the 
memory of one whose presence once honored this hall 
wherein we are met, and whose work has won for him 
an imperishable name. 


AIR-GAP, effect of, in magnetic 
circuit, 221 

effect of, on magnetic reluctance, 

117, 119, 144 

Andre, equalizing the pull of a mag- 
net, 258 

Ampere, researches of, 1C 
Ampere turns, calculation of, 166 
Arago, researches of, 16 
Arc lamp mechanism, 54 

Brockie-Pell, 250 

Brush, 253 

De Puydt, 260 

Duboscq, 263 

Gaiffe, 248 

Giilcher, 273 

Paterson and Cooper, 250, 260 

Pilsen, 247 

Serrin, 263 

Thomson-Houston, 264 

West on, 253 

Armature, effect of, on permanent 
magnets, 200 

effect of shape, 80 

length and cross-section of, 196 

position and form of, 197 

pulled obliquely, 259 

round vs. flat, 197 
Aron, sheath for magnet coils, 278 
Ayrton, distribution of free magnet- 
ism, 109 

magnetic shunts, 13 
Ayrton and Perry's coiled ribbon 
voltmeters, 255 

tubular electromagnet, 254 

T3 AR electromagnet, 49 

J' Barlow, magnetism of long 

bars, 151 

Barlow's wheel, 16 
Battery grouping for quickest action, 


resistance for best effect, 78, 185 
used by Sturgeon, 18 
Bell (A. G.), iron-clad electromagnet, 


Bernoulli's rule for traction, 98 
Bidwell, electromagnetic pop-gun, 


measurement of permeability, 68 
Bosanquet, investigations of, 90 
magneto-motive force, 12 
measurement of permeability, 


Brett, polarized magnets, 266 
Brisson, method of winding, 184 
Brockie-Pell, differential coil-and- 

plunger, 250 

Brown and Williams, repulsion mech- 
anism, 273 

Bruger, coils and plungers, 244 
Burnett, equalizing the pull of a 
magnet, 2L9 

/~"1 AMACHCTS electromagnet, 202 
^-^ Cancels electromagnet, 202 
Cast iron, magnetization of, 56 
Clark, electromagnetic tools, 277 
Coil-and-plunger coil, 251 

diagram of force and work of, 235 

differential, 250 



Coil-and-plunger electromagnet, 50, 
222, 228, 242, 244 

modifications of, 250 
Coil moved in permanent magnetic 

field, 270 
Coils, effect of position. 192 

effect of size, 191 

how connected for quickest ac- 
tion, 213 

Coned plungers, effect of, 246 
Cook's experiments, 38 
Cores, effect of shape, 80 

determination of length, 154 

effect of shape of section, 193 

hollow versus solid, 78 

lamination of, 207, 213 

of different thicknesses, 243 

of irregular shapes, 248 

proper length of, 94, 118 

square versus round, 78 

tubular, 158 
Coulomb, law of inverse squares, 111 

two magnet ic fluids, 9 
Cowper, lamination of cores, 207 

range of action, 225 
Gumming, magnetic conductivity, 10 

galvanometer, 16 
Curves of hysteresis, 75 

of magnetization and permeabil- 
ity, 71 

T~\ 'ARSON VAL, galvanometer, 270 
* ' Davy, mode of controlling 

armature, 261 
Davy, researches of, 16 
De La Rive, floating battery and coil, 


magnetic circuit, 10 
Deprez, electric hammer, 256 
Diacritical point of magnetization, 74 
Diamagnetic action, 255 
Dove, magnetic circuit, 10 
Dub, best position of coils, 192 

cores of different thicknesses, 243 
distance between poles, 194 

Dub, flat vs. pointed poles, 125, 127 
magnetic circuit, 10 
magnetism of long bars, 152 
polar extensions of core, 126 
thickness of armatures, 158 

Du Moncel, best position of coils, 192 
club-footed electromagnet, 189 
distance between poles, 194 
effect of polar projections, 198 
effect of position of armature, 151 
electric motor, 256 
electromagnetic pop-gun, 205 
experiments with pole-pieces, 132 
length of armatures, 158 
on armatures, 197 
tubular cores, 159 

THLECTRIC bells, 275 

Jr^ invented by Mirand, 274 

Electric indicators, 275 

motors, not practicable, 225 
Electromagnet, Ayrton and Perry's, 

bar, 49, 188 

Camacho's, 202 

Cancels, 202 

club-footed, 189 

coil-and-plunger, 50, 222 

coils, resistance of, 78 

design of, for various uses, 9 

Du Moncel's, 189 

Fabre's, 135 

Faulkner's, 135 

first publicly described, 7, 17 

for rapid working, 195 

Gaiser's, 253 

Guillemin's, 135 

Henry's, 27 

Hjorth's, 224 

horseshoe, 49, 188 

Hughes', 195, 267 

in Bell's telephone, 135 

invented in 1825, 16 

iron-clad, 50, 78, 133, 135, 188 

Jensen's, 191 


Electromagnet, Joule's, 39, 46 

law of, 8 

long vs. short limbs, 154 

of Brush arc lamp, 207 

Radford's, 46 

Roberts', 46 

RolofTs, 254 

Romershausen's, 135 

RuhmkorfTs, 204 

Smith's, 253 

Stevens and Hard}', 252 

Sturgeon's, 18 

Varley's, 188, 202 

Wagoner's, 204 

without iron, 251 
Electromagnetic clutch, 273 

engines, 223 

inertia, 187, 208 

mechanism, 222, 270 

pop-gun, 205 

repulsion, 208 

tools, 277 

vibrators, 274 
Electromagnets, diminutive, 100 

fallacies and facts about, 77 

for alternating currents, 206 

for arc lamp (see arc lamp 

for lifting, 52 

for maximum range of attrac- 
tion, 203 

for maximum traction, 03 

for minimum weight, 203 

formulae for, 74 

for quickest action, 209 

for traction, 41, 52 

heating of, 76 

in telegraph apparatus, 207, 221 

saturation of, 44 

specifications of, 185 

to produce rapid vibrations, 53 

with iron between the windings, 

with long versus short limbs, 79, 
171, 220 

Elphinstone, Lord, application of 
magnetic circuit in dynamo design, 

Equalizing the pull of a magnet, 258 
Ewing, curves of magnetization, 57 
hysteresis, 75 

maximum magnetization, 72 
measurement of permeability, 

59, 63 
on effect of joints, 155 

FABRE, iron-clad electromagnet, 
Faraday, lines of force, 11 

rotation of permanent magnet, 

Faulkner, iron-clad electromagnet, 


Forbes, electromagnetic brake, 272 
formulae for estimation of leak- 
age, 144 

magnetic leakage, 13 
polarized apparatus, 269 
Frolich, law of the electromagnet, 73 
Froment s equalizer, 260 
vibrating mechanism, 274 

AISER'S electromagnet, 253 
Galvanometer coils, 270 


Gauss, magnetic measurements, 113 
Gloesner, polarized magnets, 266 
Grove, range of action, 225 
Guillemin, iron-clad electromagnet, 

TT ACKER'S rule for traction, 98 
*"* Hankel, magnetism of long 

bars, 152 
Hankel, working of coil-and-plunger, 

Heating of magnet coils, 96, 98, 173, 

174, 175, 176, 183, 204, 207, 208, 257 
Heaviside, magnetic reluctance, 82 
Helmholtz, law regarding inter- 
rupted currents, 8 



Henry's first experiments, 27 
Hjorth's electromagnet, 224 

polarized magnets, 266 
Hopkinson, curves of magnetization, 

design of dynamos, 13 

maximum magnetization, 72 

measurement of permeability, 

59, 63 

Horseshoe electromagnet, 49 
Houdin's equalizer, 262 
Hughes, distance between poles, 194 

magnetic balance, 59 

polarized magnet, 267 

printing telegraph magnets, 194, 


Hunt, range of action of electromag- 
nets, 224 
Hysteresis, 75 

viscous, 77 

IRON-CLAD electromagnet, 50, 78, 
133, 135 

range of action, 249 
Iron, magnetic qualities affected by 

hammering, rolling, etc., 77 
maximum magnetization of, 92 
permeability of. 92 
permeability of, compared with 

air, 85, 118 
the magnetic properties of , 54, 56 

TENSEN'S electromagnet, 191 
J indicator, 275 
Joints, effect of, on magnetic reluc- 
tance, 155 
Joule, experiment with Sturgeon's 

magnet, 20 

lamination of cores, 207 
law of mutual attraction, 40 
law of traction, 100 
length of electromagnet, 94 
magnetic saturation, 56 
maximum magnetization, 72 

Joule, maximum power of an elec- 
tromagnet, 11 

range of action, 225 

researches, 39, 81 

results of traction experiments, 

tubular cores, 158 

TT^APP, design of dynamos, 13 
-**. maximum magnetization, 72 
Keeper, effect of position on tractive 

power, 78 
effect of removing suddenly, 78, 


Kirchhoff, measurement of permea- 
bility, 59 

Krizik, coned and cylindrical plung- 
ers, 247 

T- ANGDON-DAVIES' rate gover- 
M nor, 275 

suppression of sparking. 279 
Laplace, two magnetic fluids, 9 
Law of inverse squares, 13, 78, 110, 
112, 226, 251 

a point law, 111 

apparatus to illustrate, 113, 115 

defined, 111 

Law of the electromagnet, 73 
Law of the magnetic circuit, applied 
to traction, 87 

as stated by Maxwell, 88 

explanation of symbols, 82 
Law of Helmholtz, 209 
Law of traction, 71, 100, 101, 102 

verified, 90 
Leakage of magnetic lines, 85, 1 8, 

110, 112, 129 

Leakage reluctances, 148 
Lemont, law of the electromagnet, 73 
Lenz, magnetism of long bars, 151 
Leupold, winding for range of ac- 
tion, 248 

Lines of force, 11, 55 
Lyttle's patent for winding, 184 



MAGNETIC adherence, 271 
balance of Prof. Hughes, 59 
brake, 272 

centre of gravity, 112, 113 
circuit, 10,11, 12, 13,47 

application of, in dynamo de- 
sign, 12, 13 

for greatest traction, 97 
formulae for, 86, 87, 101, 102 
tendency to become more 

compact, 123, 204 
various parts of, 49 
conductivity, 10, 11, 83 
field, action of, on small iron 

sphere, 255 

flux, calculation of, 83, 164 
gear, 271 
insulation, 84 
leakage, 13 

calculation of, 122, 161 
calculation of coefficient, 168 
coefficient of, "v, 11 145 
due to air-gaps, 120, 144 
estimation of, 144, 150, 169 
measurement of, 137 [193 
proportional to the surface, 
relation of, to pull, 139 
memory, 172, 221 
moments, 13, 87, 158 
output of electromagnets, 185 
permeability, 11, 54, 83 
polarity, rule for determining, 51 
pole of the earth, 113 
reluctance, calculation of, 3, 95, 


of divided iron ring, 117 
of iron ring, 117 
of waste and stray field, for- 
mulae for, 146, 150 
resistance, 12, 82 
saturation, 47, 56, 58 
shunts, 13 
Magnetism, free, 9 

of long iron bars, 151 
Magnetization and magnetic traction, 
tabular data, 89 

Magnetization, calculation of, 161, 164 

defined, 87 

internal, 9, 54 

internal distribution of, 63, 78, 138 

of different materials, 57 

surface, 9, 13, 48 
Magnetometer, 114 
Magneto-motive force, 11, 12, 81 

calculation of, 82, 83 
Maikoff and De Kabath, repulsion 

mechanism, 274 
Marsh, first vibrating mechanism, 274 

vibrating pendulum, 16 
Maxwell, galvanometer, 270 

law of the magnetic circuit 
stated, 88 

law regarding circulation of al- 
ternating currents, 8 

magnetic conductivity, 11 
Mirand, inventor of the electric bell, 


Mitis metal, magnetization of, 72 
Moll's experiments, 22, 34 
Moseley's indicator, 275 
Mttller, law of the electromagnet, 73 

magnetism of long bars, 152 

measurement of permeability, 58 

NEEF, vibrating mechanism, 274 
Newton's signet ring load- 
stone, 100 
Nickles, classification of magnets, 


distance between limbs of horse- 
shoe magnet s, 158 
distance between poles, 194 
length of armatures, 158 
magnetic brake, 272 
magnetic gear, 271 
traction affected by extent of 

polar surface, 104 
tubular cores, 158 

approach, 258, 263 
Oersted's discovery, 16 
Ohm's law, 8, 12, 26, 81, 209 



PAGE, electric motor, 256 
sectioned coils, 256 
electromagnetic engine, 223 
Paine, sheath for magnets, 278 
Permanent magnets contrasted with 

electromagnets, 199 
uses of, 264 
Permeability, calculation of, 163 

methods of measuring, 58 
Permeameter, 70 
Permeance, of telegraph instrument 

magnets, 150 

Perry, magnetic shunts, 13 
Pfaff , tubular cores, 158 
Plungers, coned vs. cylindrical, 247 

of iron and steel, 244 
Point poles, 114, 115 

action of single coil on, 230 
Poisson, two magnetic fluids, 9 
Polar distribution of magnetic lines, 


region, defined, 112, 113 
Polarized apparatus for indicators, 


mechanism, 264 

Pole-pieces, convex versus flat, 79, 104 
Dub's experiments with, 126 
Du Moncel's experiments with, 

effect of position on tractive 

power, 79 

effect on lifting power, 78 
on horseshoe magnets, 198 
Poles, effect of distance between, 194 

flat vs. pointed, 125, 127 
Preece, self-induction in relays, 218 
winding of coils, 184 

IT) adford's electromagnet, 46 
-*- ^ Range of action of electromag- 
nets, 224, 225, 248 
Rate governor, 275 
Reluctance, 12, 82 
Repulsion mechanism, 273 
Residual magnetism, 67 

Resistance of electromagnet and 
battery, 185 

of insulated wire, rule for, 176 
Ritchie, magnetic circuit, 10 

steel magnets, 172 
Roberts 1 electromagnet, 46 
Robertson, galvanometer, 270 
Roloff s electromagnet, 254 
Romershausen, iron-clad electro : n ag- 

net, 135 

Rowan, electromagnetic tools, 277 
Rowland, analogy of magnetic and 

electric circuits, 12 

first statement of the law of the 
magnetic circuit, 81 

magnetic permeability, 11 

maximum magnetization, 72 

measurement of permeability, 

59, 63 
Ruhmkorff 's electromagnet, 204 

O ATURATION, curve of, 153 

distribution of, 138 
effect of, on permeability, 118 
Schweigger's multiplier, 16, 28 
Sectioned coils with plunger, 256 
Self-induction, effect of, 217 

in telegraph magnets, 214, 218 
Siemens, differential coil-and-plung- 

er, 250 
relay, 270 

Siphon recorder, 270 
Smith, plunger electromagnet, 253 
Sparking, suppression of, 277 
Steel, magnetization of, 58 

permeability of, 61 
Stephenson, electric motors not 

practicable, 225 

Stevens and Hardy, plunger electro- 
magnet, 252 

Stowletow, measurement of permea- 
bility, 59 

Sturgeon, biographical sketch, 17 
experiments on bar magnets, 125 
experiments on leakage, 122 



Sturgeon, first description of electro- 
magnet, 7, 17 

magnetic circuit, 10 

polar extensions j 132 

polarized apparatus, 266 

portrait wanted, 27 9 

tubular cores, 158 
Sturgeon's apparatus lost, 20 

first electromagnet, 18 

first experiments, 20 
Surface magnetism, 108, 109 

r MIME-CONST ANT of electric cir- 

- cuit, 211, 213, 216, 218 
Thomas, wire gauge table, 178 
Thomson (Elihu), electromagnetic 

phenomena, 208 

(J J.), on effect of joints, 155 

(Sir Wm.), current meters, 255 

polarized magnets, 266 

range of action, 225 

rule for winding electromagnets, 

siphon recorder, 270 

winding galvanometer coils, 257 
Thorpe's semaphore indicator, 275 
Traction, formula for, 98 

in terms of weight of magnet, 98 
Tractive power of magnets affected 
by surface contact, 135, 151 

integral formula for, 89 
Treve, iron wire coil, 248 
Tubular coils, action of, on a unit 
pole, 232 

attraction between, 243 

winding of, 256 

Two magnetic fluids, doctrine of, 9 
Tyndall, range of action, 225 


ARLEY, copper sheath for mag- 

net coils, 27H 
electromagnet, 202 
iron-clad electromagnet, 188 

Varley, polarized magnets, 266 
Vaschy, coefficients of self-induc- 
tion, 218 
Vibrators, 274 

Vincent, application of magnetic cir- 
cuit in dynamo design, 12 
Viscous hysteresis, 77 
Von Feilitzsch, plungers of iron and 

steel, 244 

magnetism of long bars, 152 
measurement of permeability, 59 
tubular cores, 158 
Von Koike, distribution or magnetic 

lines, 137 

Von Waltenhofen, attraction of two 
tubular coils, 243 

WAGENER'S electromagnet, 204 
Wagner, vibrating mechan- 
ism, 274 
Walmsley, magnetic reluctance of 

air, 148 
Wheatstone, Henry's visit to, 38 

equalizer for telegraph instru- 
ment, 264 

oblique approach, 259 
polarized apparatus, 266 
Winding a magnet in sections, 256 
calculation of, 95, 173, 183, 190 
coils in multiple arc, 258 
differential, 278 

effect of, on range of action, 248 
for constant pressure and for 

constant current, 182 
iron vs. copper wire, 202 
of tubular coils, 256 
position of coils, 193 
size of coils, 191 
thick versus thin wire, 78 
wire of graduated thickness, 257 
Wire gauge and ampereage table, 


Wrought iron, magnetization of, 56, 
. 64,65